Let's fold the hand pre-flop. Especially if the big blind lost most of his stack recently, those chips are going into the middle very often and you'll be stuck playing a multi-way pot for a decent amount of your stack with 95s.
In addition to that reasoning, 95s is just a bad hand. It's barely in the top 50% of
hands, and with multiple players yet to act, it's not going to cut it most of the time. You're basically hoping to flop a non-dominated flush, trips, or two pair to even have a playable hand!
On the flop, I like the check-through. The side pot is totally dry, so you have little motivation to semi-
bluff, even though your hand is likely one of the worst ones in terms of absolute strength at the time, e.g. 9 high is bad, but the open-ended straight draw is decent. Your
equity matters little though, given the dry side pot. In other words, if you force everyone else to fold, you're almost always at least a 2-1 underdog to the all-in player.
On the turn, you should be betting. You have a solid
bluffing opportunity and obviously the ability to represent bluffs since you're playing the top 50% of hands in this spot! When you simply check and call, you do allow other players to continue to bluff. At the same time, what can he put you on once you call such a small "please call me" type bet? It looks like you have a straight. Also, remember the chat about the dry side pot? You're checking to the last to act player in the hand in a spot where he has very little motivation to bluff, so why not do the betting yourself and hope Ax hands call you down for 2 streets, rather than represent a straight by checking and calling and allowing your opponent(s) to play very well against your hand.
On the river, jamming completely defeats the purpose of calling the turn. When you call the turn, it should be with the intention of inducing more bluffs from the in position player. Moving in is almost never going to be called by a worse hand. All evidence in the hand points toward you having a straight. The best you're hoping to do is to fold out a chop if the other player has a 5, and even that is unlikely. So when you bet, you're either splitting the pot when called, losing when called, or folding out a worse hand than your straight. When you check and call, you might chop with another straight, you might lose to the nuts, but you can also win money from inducing a bluff; therefore, checking is best.
It's unreasonable to assume any of these players is playing 75s and to be worried about that specific hand. If any of these guys have 75s, then that certainly means that they're playing FAR more hands that you beat. The fact that you lost the hand is simply unlucky; but, that isn't the issue here. There are many ways you can improve your play in this hand and in this spot.
Start by just tossing 95s, but the logic of how the hand is played post-flop can definitely be extrapolated to other hands in similar spots, especially the "don't move all-in with the near nuts when you very much don't appear to be bluffing and your opponent won't call you with a worse hand" bit.
