The space between my house and the fence is 5 ft.

A tree capable of giving you useful shade would be way too big and would damage your roof. You need a vine on a trellis.

Build a sturdy trellis in panels (2x4 lumber, sandwiching lattice) and attach it to the wall just inside the eaves line, then plant a variety of vines that love sun.

Beware of the monsters like Lady Banks Rose, catsclaw and wisterias - they will eat the house.

Better choices: Snail vine, Queen's wreath, Hardenbergia, Mascagenia (yellow orchid vine), flame flower ... check the Sunset Garden Book for Zone 13 vines. I plant several vines that bloom at different times of year and let them fight for space.

OR ... screw a bunch of cup hooks or screw eyes into the top of the wall, lay a redwood 2x4 at the base of the wall with more screw eyes, and run jute twine between them in a diamond pattern. Plant vines like Queens wreath that die back in the winter. When it dies, you can clip the vines at ground level, cut the strings, roll it up and toss it on the compost heap. My parents did that for years. By the middle of May they had vines that shaded the west, but in the winter they had exposed wall for heat gain.

I have a pomogranate tree in a 4 foot space, they dont give much shade but filters some sun out. They lose leaves in winter. Also have an orange jubilee plant that has grown to a small 10 foot tall tree. Go for a walk in the neighborhood see what others have planted in the west side 5 foot space you will get ideas.

Lazygardens, IME, Hardenbergia won't take a west exposure like that--It may survive, but it will really turn yellow in summer. Also remember that not all of the Sunset picks will take afternoon sun, and Sunset won't know which do!

To add to the sun list: 'Madame Galen' Trumpet Creeper (bare in winter to let sun through), Pink Trumpet Creeper, Carolina Jessamine (with soil sulfur and plenty of water), European Grape or 'Roger's Red' California Grape (both also deciduous), and Hacienda Creeper.

Kevin : )

We live in Peoria in a North facing house and we too wanted a shade tree. We went to Elgin Nursery and Tree Farm on McDowell Rd. The guys at Elgin were very helpful and in the end we chose a lovely Hong Kong Orchid Tree. At maturity, the tree will have a canopy up to 20ft, and on top of that - it's dripping with lovely plummy-pink orchids. It's a lovely tree that we believe will more than meet our needs.

Ice cream bananas which can reach fifteen feet would be great for shade if you had multiple plants.

I wonder if your Hong Kong Orchid is a Desert Willow or a Catalpa Tree?

Cindy - "Orchid trees" (various Bauhinia species) grow pretty well in this area if they get protection from frost for thew first few years.

Orchid trees grow easily from seed. I've grown several that way. I start them in a container so I can protect them from frost and put them in the ground when they're about 5' tall. I even hauled one six-footer around NoCal and Oregon as a houseplant. :o)

I think it might be a good choice for your side yard.

Orchid tree is way to massive for that small a side yard. Any tree, the trunk alone is big so needs to be planted more than 2 1/2 feet from the wall, which is half the space you have.
Pomegranate can, and will need to be, hedged fairly often, but may be ok. Still don't plant it to close to the house and it will make it a little tight getting past it when it's growing out between trimmings.
Crape Myrtle may work. It's a little slow growing so it will take time before it covers major portion of the height, but that is also exactly why it may be manageable for the space. It's more bush than tree, very small "tree" and multi-trunked. Prune once each winter and light shaping if a branch takes off the wrong direction. They have wonderful blooms.
I rather like the idea of trellised vine for that space. 5 feet is just too tight for any tree really. If you do Christmas tree lights, you can cut when it's time to put up your lights and put up new string when you take the lights down.