2G iPod touch with iOS 4.2.1
The 2nd generation iPod touch can’t be upgraded to iOS 5.

One PDF reader that still works on pre-iOS&nbsp;5 devices is GoodReader, although according to their site it requires iOS&nbsp;4.3.

If you connect your iPod touch to iTunes, then there should be an option to update to iOS&nbsp;4.3. The instructions in this Apple Support article explain how to update an iOS&nbsp;4 device (see Update your device using iTunes).

There may be other PDF readers that can run on iOS&nbsp;4 devices, but I don’t know of any by name. Pre-iOS&nbsp;5 devices are now a very thin sliver of the iOS installed base, so most developers have dropped support for them.