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)