Definitely try hitting the starter with a hammer. Be firm with your hit, not too gentle.
Also, when you first turn the key to ON, does the check engine light come on? If not, you may need to replace the capacitors in your computer.
Could you clear up some ambiguity with your description? You bump started the vehicle, then you ran it for 5 minutes and turned it off, or did you run it for 5 minutes and then it died?