Possibly, but not necessarily; theoretically, You could get a 5 and a 10 and stay in the game, but you could also get a 5, kicked out, and suspended for subsequent games. I think there may be software limitations on the online box scores to capture the various layers of discipline that are now part of the rules.
My understanding is that a player can (1) get a 10-minute "misconduct" penalty (in addition to other simultaneous infractions) and return to the same game; (2) get a "game misconduct" (i.e. ejection) and still play the next game; or (3) commit a 5 minute major penalty where the referee has discretion on whether to assess a "disqualification" which is an ejection plus have to sit out the next game (or more if repeat offender). Some of the nuances came up when I was watching the Brown/Yale game for a bit last night, and one Yale player got a 5 minute major for a hit from behind, but was allowed to stay in the game. In the next period, a different Yale player got a 5 minute major but was disqualified for a slew foot, and has to miss the next game. The ESPN+ commentators didn't really explain the difference, but the section in the rules is here:
https://www.achahockey.org/wp-content/uploads/sites/2/2021/07/2020-22-NCAA-Rules.pdf#page=34