FFV's job system is taken from FF3 in the first place. If it's taken from an FF, it is from FF3. FF5 is the wrong answer no matter what.
But the job system in Tactics, especially the way classes grow, is taken from Tactics Ogre, which is taken from Ogre Battle.
Saying FFV's job system came from III is a huge stretch. FFIII's system probably has more in common with FFVI in terms of game impact. The classes you chose were meaningless after you switched out of them, and ultimately got replaced by superior versions originally although the remake for the DS changed that a bit. The concept of abilities transfering over and having a use for being a class beyond the immediate was introduced into the FF continuity by V.
Also worth noting that Final Fantasy V was released 3 tears before Tactics Ogre, so really that can never be the right turn of things. If anything Tactics Ogre got the concept from FFV.
Edit: Oh I see you meant Ogre Battle which was released in 93 rather than 92 as with FFV. Clearly the two idea were developed side by side and independent of each other then.