I agree; on my 5, iOS 9 is very choppy in multitasking and spotlight search too. Looks like that's everyone's sore area.iPhone 5 feels slightly more sluggish under 9.0 than 8.4.3 or whatever the final 8 release was (I can't remember).
Specifically, animation transitions aren't as smooth in multitasking, control center, and spotlight search. The stutter can be pretty bad.
Overall though, 9.0 is useable. It's just not as pleasant as it should be. I'm thankful though that the keyboard shift at least changes the key capitalization of the keys now.
I downgraded back to iOS 8.4.1. When I get my preordered 6s, I'll be selling my current 5, and it may help some people buying the used 5 if iOS 8 was on it instead of 9, especially at a .0 version. Now, I just gotta bite my tongue and ignore the big bright red (1) on the Settings icon.