Can I run iOS 5 Apps on my iOS 3.1.3 iPod touch? I have an iPod touch 1G running iOS 3.1.3, and I really want to get iOS 5 Apps on it. Is there a way to do this? Can I do it without using a computer?
You can't run applications made for newer versions of iOS on 3.1.3.  They rely on features, APIs, and potentially even hardware that do not exist on your old iPod.

Here is further discussion on why this is generally not possible - even when you jailbreak an iOS device.