This "5 & fly" is a quite frustrating flaw in the Twins overall strategy! So many games last year, Gray and Ryan, & probably several others were pulled when they had several more gettable outs left in the tank.
I say give the guys a chance, at least over the first few starts of the season. Let 'em prove it, either way. Doing so would put faith in the players' ability, and not strict adherence to some mindless algorithm or spreadsheet formula.
You can see on better-coached teams (think Francona last season, for example, maybe Showalter also) when it "feels" like the pitcher was on a roll or could squeeze out of a jam, they leave the guy in and it pays off. Whereas, the Twins or other teams with a quick hook (Rays, Yankees, probably most other teams actually) bring in some bullpen piece, supposedly a favorable matchup, who quickly gives up the bases-clearing XBH. Obvious exception is postseason, but regular season should give the nod to the starter unless it's someone like Archer, Odorizzi, Syndergaard, HIll, Greinke, etc. who's got no business going past the 5th.