You're using Flash CS5 so you're only going to be able to compile for iOS. CS5.5 outputs AIR for iOS and AIR for Android as well as Blackberry Tablet (FB).
Make sure you've overlayed the latest AIR 3.1 SDK on your version of flash and your CS5 is up to date.
Going the AIR route or using Flash Builder (or elipse fdt for free) will be a better albit more complex route but will yeild far better results. The only thing CS5 is really good for is it does not use AIR therefore apps can be built for 3g devices. However most of the things you care about are in AIR (GPU accel video, etc) and you'd be doing yourself a favor to update to Flash Builder.
You can still use Flash CS5 to craft your assets in the library. Then you simply export a SWC of them and reimport into Flash Builder and code it from there.
FWIW I never had your issue in Flash CS5 when I just started dabbling with iOS apps.
Thanks -- can you tell me what you mean by this:
"Make sure you've overlayed the latest AIR 3.1 SDK on your version of flash"
I'm also confused by, "The only thing CS5 is really good for is it does not use AIR."
BTW I am developing for WIndows desktop, not for phones.
Anyhow to overlay air please follow the directions in this link. That will update the AIR in Flash CS5.5 to the latest release version. If seems like a hassle but once you've done it it's a cinch to do it again and again as new AIR releases come out.
Disregard the CS5 comment versus CS5.5 as it doesn't make a huge difference to AIR Desktop. Only AIR Mobile.