Android - Is it possible to have multiple instances of the same app (logged in to different accounts)?

There's an awkward solution:

Renaming the package name inside an apk as proposed by Adobe to fix a nasty limitation of their AIR framework, XDA has proposed the same too.

All use apktool to reverse engineer an app (unpack apk, change package name in AndroidManifest.xml, repack, resign).

Note:
This won't change locations on the SD card though (if it's used, all 5 instances would use the very same folder on the card still, just FYI)

Just decompile the app, change package name, compile, push to phone. Done! Just dont distribute it, advertising it as yours, because that is illegal.

Titanium Backup PRO (and only the paid (Pro) version allows this) - FYI ROOT REQUIRED - does allow Profiles, but not the running of multiple insntances of the same app, with the exception of Winamp (but Winamp has Always been written to do that, no matter the platform)