Rhubarb? Will Fatsia survive for you? You could try coppicing some trees such as Paulownia and Catalpa to get huge leaves and no seed pods. Works on Platanus too.

I'm in the same zone,and this spring I'll be planting and then trying to overwinter with some protection the following plants -Musa Basjoo, Southern Magnolia(Edith Bogue and BBB), prickly pear cactus, Crepe Myrtle(Dynamite), hardy dinnerplate Hibiscus and Gunnera Mannicata.

I like the look of fatsia and basjoo - I may try those. I have rhubarb but always end up eating it! I tried a crepe myrtle that a friend brought up north. I planted it in an area enclosed on three sides and protected but it didn't overwinter. I'm not sure which variety it was. Thanks for the ideas - the catalogs are now arriving in the mail and I have a plan!

Cannas are easy to dig up and you should definitely try elephant ears.
Castor beans can be grown by seed in late spring and grow to 10 feet tall (or more) by fall even in your zone 5! The purple ones are my personal favorite, but keep in mind they are very poisonous plants when eaten so I would not plant them where pets or kids can get them.
Elephant ears need to be dug up every year like cannas, but they look great. Thailand Giant is a great cultivator for large leaves, but just the typical green colocasias grow very well for me and get large! Elephant ears come in lots of different colors, shapes and sizes and the leaves are definitely large and tropical looking.
As far as bananas go, Basjoos survive the winter for me without any help but they just aren't great growers. The tropical bananas are faster growing for me and seem to do better. You have to dig them up every year but they stay dormant indoors so like cannas and elephant ears, they will not take up too much room. Ensete ventricosum (Red) are one of my favorite bananas. They wont make edible fruit but when planted with the right plants the color is really nice.

Brugmansias are great plants too! If you get one that is healthy they will grow really fast. Mine was only a foot tall when I got it in October 2010, but with a lot of fertilizer (they love water and fertilizer during warm weather) it grew and bloomed really well. Sometimes it can have 20 blooms on it at once and the fragrance at night is incredible! Mine is about 7 feet tall now. Here's a pic of it in bloom. This was when it was in between flushes of blooms, every few weeks it has a lot of flowers on it and in between that it has a little bit less.

Here are a few other pics of the plants in my yard with big leaves...
Butterfly ginger with a alocasia (common name is Persian Palm) in background.

Plants by the pool area including a blue java banana, potted majesty palm, the ginger, and the alocasia.
http://i705.photobucket.com/albums/ww59/tropicalzone7/My%20Yard%202012/IMG_7039_zps75699086.jpg
This is a hardy passion vine which survives the winter in my zone 7 and might survive the winter by you too. Its evergreen in my climate and is actually a little invasive. It's one of the most tropical looking flowers in my yard even including the actual tropical plants in my yard!

The biggest plant by my pool is definitely my elephant ear. Just some miracle gro and water and it got huge, its just a normal green variety.

Dragon wing begonias are one of my favorite annuals. The leaves are nice and large and they are always in bloom. They do well in sun but are easier to take care of in part shade during the hottest part of the summer.

In this pic I have some spiral gingers, an alphina ginger, and a musa saba. All of these plants are dug up in late fall (the palm in the bottom of the pic is a European fan palm and that stays out all winter)

This is my largest Plumeria. It's a potted plant, but the blooms are beautiful and so are the leaves. I got it as a 1 foot tall plant in March 2009 and now it's over 12 feet tall. This is a really fast growing plumeria, my others are not as fast growing as this one!

Here's a look from above

Here's what you can do with potted tropical plants

A lot of my yard is potted tropicals since I dont have a lot of room in the ground for other plants.

I hope this gives you some ideas!
-Alex

Wow... your yard is GORGEOUS! Absolutely everything looks so happy and healthy.
I want this same lush tropical look (in Florida) Where do you begin?

My Elephant Ears don't seem to like much sun at all. Harumph!

Thanks a lot! I appreciate the compliment! I just bought a bunch of plants I liked and figured out where I thought they looked good. I've only been growing a lot of tropicals since 2009 (I had tropical plants for years before that, but not much more than you'd expect in a summer landscape).
Sometimes it's better not to have too much room since it keeps you from buying a crazy amount of plants and it also makes the lush look a lot easier. The great thing about Florida is that you dont have to worry much about cold weather, but that would be a challenge for me because my plants would crowd each other pretty quickly if I lived in a frost-free climate.
My Elephant ears also give me a hard time in too much sun and that's in NY! Mine get a LOT of water and direct sun from 9am to 3pm during most of the summer. If I miss out on a day of watering it usually starts to wilt, they love water and heat but only when they are both combined!

Thanks for looking!
-Alex

I agree about yard size. I've got 3/4 of an acre that's mostly empty and I'm trying to get YOUR look. It will take a while.
Hey, can you show the size of the pot you have your Plumeria in? I decided to pot mine for the patio, but I want them to stay in the pot I put them in and not need something wider, deeper, or whatever.

I looked through all my photobucket pics and I cant find any that show the pot size of my plumeria. I'm not home right now otherwise I would post a pic of it! Plumerias are good with pot size since you can always prune them back to keep them smaller and you can do a good root pruning every few years. There are also some nice dwarf cultivators that do great in pots. Here's my plumeria divine. It reliably blooms every summer and will never outgrow this pot (but I may replace some of the soil with fresh soil this spring. The Plumeria divine is in the bottom right side of the pic (this pic was taken in 2010)

-Alex

Yeah, my Plumeria don't do that. Or they haven't yet. I think they weren't getting enough sun? I put them in a pot today and out in fulllllll sun. One is a 2-foot-tall "stick" with no branches and one 7" leaf on it, the other is a 5-foot-tall "Y" shape with the barest indication it might try to grow leaves. They're ridiculous.
I could just drool over your pictures. I wish you could come do that to my house. LOL!

Thanks again! Glad that you like my yard! Your 2 footer might bloom this summer, it sounds like it's getting old enough. The one with the Y shape on ti already bloomed and depending on the cultivator, it will probably bloom soon too! Lots of sun helps a lot. A lot of people give their plumerias fertilizer that helps promote flowering, but I pretty much let mine do their own thing. I sometimes give it some seaweed extract in early spring so it can start growing leaves (they take a little over a month to start looking full again). Mine all get a lot of full sun and they love it. Definitely make sure that they dont dry out too much in full sun. They do like drying out a little bit but the Florida sun is a lot more intense then the sun in NY.
-Alex

Here are what mine look like today. The tall "Y" has never bloomed. It gets 2-3 leaves that fade and fall off. The 2' was just given to me last week. Hoping the problem was the sun!

There are some truly hardy plants with large tropical-looking leaves, for instance Magnolia macrophylla, which would likely do fine in Ohio zone 5.

I really like M. macrophylla eric, great northern tree for the tropical look!

Your plumeria looks like it's pretty healthy. Not sure why it's not making more leaves than that. It probably needs more sun and less water. They go dormant this time of the year so they are supposed to be bare until warmer weather returns (mine start growing in April at the earliest and some dont break dormancy until May!).

Is the 2 foot tall plumeria the one that is in that pot now? I would plant it in it's own pot. They like being root bound, but they dont like being planted too close together (although I know that you are probably trying to get some more foliage for the bottom of the plumeria. Now that my plumeria is starting to get taller I'm thinking of mounting some orchids or bromelaids onto the trunk to make it look full even where it isnt growing anymore so you can do that with yours too if you're looking to make the trunk look more interesting!
-Alex

This is a sort of "experiment" to see what happens now that they're in full sun. Both have little tips of new leaves emerging, so if they seem like they'll thrive, I'll give it its own pot. (Turns out the leaf on the 2' tall one is left over from last summer. Still green. Strange)

Definitely a good sign if they both are showing signs of growth! They should be looking really nice in a few months. Sometimes they do keep a leaf or 2 from last year, most of mine go completely bare but I always have 1 or 2 of my plumerias manage to keep a few leaves and some even grow new ones while indoors over the winter.
-Alex