Shoving pre would most likely be +EV and unexploitable according to Nash, but it's not likely to be the best option.

The reason is that there are only two likely eventualities, broadly speaking, that can happen once you minraise:

1. The players behind you are 3-betting/shoving on you infrequently with tight ranges, making a minraise very profitable because it gets through very often, but making a call very unprofitable.

2. The players behind you are 3-betting/shoving on you more frequently, making a minraise slightly less profitable because it gets through less often, but making a call quite profitable once you get shoved on.

So basically the bottom line is that if you're that worried about getting shoved on once you minraise, that means it's probably a good idea to call it off. If you're not that worried about getting shoved on, just fold to the shove in the knowledge the raise was super profitable in the first place.

HoldemResources Calculator could tell you the exact profitability of this one. No need to rely on approximations and 45-minute chats with friends when a fairly cheap piece of software can tell you the exact answer within 2 minutes.

I can understand the argument for folding 55 here and preferring to raise hands that play better postflop, but I think you're underestimating how well 55 plays postflop (and preflop – raise/calling the button isn't out of the question here if button is aggressive), and ignoring some crucial considerations regarding our overall frequencies in this spot.

First part – I think we would really have to be making some bad decisions postflop for 55 not to be profitable here. I can understand how it's pretty awkward if the SB has a flatting range, but the wider the BB is defending the more we're going to find ourselves in spots where we can play comfortably postflop, and the SB is probably more likely to 3-bet us given the stack sizes, which makes 55 a good candidate for a raise/4-bet shove.

Second part – in terms of the pure profitability of the open-raise, firstly a minraise usually only has to work around 46%, depending on the antes. Small difference, but significant. Secondly, cutting some of the smaller pairs out of our opening range here does have an effect on our responses to potential smaller 3-bets from other players behind, and gives us fewer hands with which we have good equity 4-bet shoving versus a reasonably balanced range. We end up raising with a range that is disproportionately heavy on blocker-type hands that might be marginally more profitable preflop (or might not) but are much less comfortable shoving versus a 3-bet or withstanding aggression from the button or the BB.

It's an interesting spot. If OP can post the raw HH then I would be curious to run it through Holdem Resources Calculator to see what we get. Bottom line is that if OOP postflop play was a significant possibility here, I would think we'd be okay folding and constructing our range differently, but when we're almost guaranteed position if we do play postflop, I'd be surprised if we can't at least capture 100% of our equity here. In position, we can likely capture around 120-130% of it if the BB doesn't play particularly well after defending wide (which most players don't).