It's a weed and you spray it with Round up and kill as much as you can before it seeds.
I have that stuff too. Irritating to say the least.
Don't be afraid of the ROund Up. Just spray it right on the leaves and try not to spray any other plant around it.
Mabey even a good weed killer for your lawn might be able to kill it, but kill it soon. If you are lucky enough to kill it before it seeds, you will have alot less of it next year.
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The one with 5 leaves is most likely Virginia Creeper which is a weed even in MD where I am. Not sure about the other one. You may need to get a weed killer that is made for perennial vines/woody plants. I've heard of one called Crossbow but have not actually used it. I may need to since I'm trying to get rid of Chinese Wisteria that was trying to pull the siding off our house!

I want to re-plant the pergola that is attached to the house but want to make sure I don;t choose such an aggressive vine again.

The 5 leafed one is virginia creeper.....the other looks like wild grape....both are vines and both have an aggressive tap root.....Round up may not kill the root completely and so may return.....You may have to spray them a couple of times this summer.......
or follow the vines back to the soil and dug them out.....dig deep!