This is a class of question that comes up sometimes on the forum that amounts to "I am a nit, how do I get value for this crushing hand I have?". An extreme example would be asking how an
OMC can get value out of his AA against a good player. It just can't be done, the correct answer is that the OMC needs to open up his range in all spots and then value for the AA will take care of itself.
I'm not necessarily accusing you of being a nit in general, but if you say that the LAG is going to fold everything except 5s to a shove and shut down if you flat, then the LAG is assuming that you will have an overpair when you play back at him. You need to make that a bad assumption. It's possible that the LAG is raising a balanced range and there's nothing you can do, but more likely he's raising too much and you need to punish him for it by pushing him off his hand. Value hands against this type of player often don't represent a chance to get value, they're just backup for the main way you win against the LAG, which is meet their aggression with aggression. Trapping with value hands is how you beat maniacs, not good LAGs.