Can dropping the iphone 5 make it run slower?

I've dropped it a couple of times but only from like 2 or 3 feet from the ground. Can that damage my iphone 5 internally?

Yes. Shock damage can loosen internal electrical connections.

Anything is possible if you did damage, but I've dropped mine a couple times on cement and it bounced… And never had an issue. I was lucky it hit right because it hit pretty hard.