What were Vietnam Enlistment Age Requirements?

I am currently researching for an upcoming TV series, set in the early 1970s.  In our show, we have several Vietnam vets who enlisted in their 40s (i.e. not drafted).  What I'm currently trying to determine: what is the oldest age someone could enlist to fight in the war?  Both men are fit and able bodied -- they would pass the physical test (if there was one) and more than handle the subsequent demands of combat.  But would the U.S. Army have accepted them at that age?