I gather she does not already have kids? Or else she would know better than to do this.
If it were me, I'd leave the kids at home and enjoy the party without them (though 175 people? Wow, that's...unheard of for a baby shower.) But if hubby insists, says "there'll be other kids there" etc., and you don't want to fight that battle, take the kids and take NEW things to distract them. Your son might find a new hand-held little game more interesting even than ripping open presents. Make it something he will really focus on for a short while and something he could do at the back of the room with you or dad nearby but not having to hover over him. I'm not saying buy him a DS or get him some expensive gift! I'm saying find something that will distract him sufficiently if that's doable. Some would say it's "parenting by bribery." Hey, maybe so. I think of it as making the best of a bad situation and keeping him from having an eventual meltdown. I'd do the same thing in a grown-up-party situation like a wedding where kids were expected to attend by people who don't realize the limitations kids have on their "best behavior."
And I'd also inform the SIL, with that big smile on your face, in advance: "It's so nice of you to include the kids" (because she does think of this as including the kids) "and we want to be sure they're ALL included, so after Billy opens a gift or two, we're going to ask him to come look at a toy so the other kids can have their turns too. That will be so nice, for all the kids to participate..." I hope she gets the hint and does not constantly call him up there over and over: "Billy, where are you, get up here, open this one.." etc. You may have to be more blunt about "You're great to include the kids but Billy gets overexcited and this is YOUR day, not his birthday, so we're going to have him play after a certain point...."
Remember, too, others attending will realize he is five. They will not think badly of you if he gets overexcited and wants to open more. I would bet all the kids will do that, especially if there are tons of gifts from 175 guests. Any guest with kids will know that you parents of the attending kids are doing your best and they will know that the SIL is not handling it well. She won't do that if there's a shower number two, I'm sure.