NiCads can be charged with a current limited source where the a current no more than C/10, that is, one tenth the battery capacity (something like 5000 mAh for a D sized NiCad, so <500 mAh). One of your 5 V sources and a 10 Ohm resistor would do this. (Edited to add) Note that this works for individual cells or cells in series (what you've described); cells in parallel should not be charged this way. "Smart chargers" use a more sophisticated algorithm and will result in longer battery life, but this gives you a simple test to see if the cells are any good.
NiCads that have been sitting around for years without being charged tend to develop internal shorts, so it's likely at least some cells are going to be bad.
Cadmium is considered a toxic/hazardous material so discarded batteries should be disposed of according to the regulations of your community. In the US the major hardware and electronics retailers (e.g. Lowes, Home Depot, Best Buy) accept such things.