I tire of D&D's stranglehold on players minds. It's slowly getting easier and easier to suggest people read a second book, and while that's great to see, we still have plenty of work to do.
And, no, for the 11th time, I will not run my Star Trek game in 5e that's insane.
Are you using the official Star Trek TTRPG? I definitely want to run something with the Lower Decks book for my party at some point. Maybe next First Contact Day
Star Trek Adventures? Yeah! It's a great book. It takes a little bit to wrap your head around, as it's a little abstract in some places, but once you get it, it's simple to play and works very well for emulating an episode of Star Trek.
I had used Mongoose's Traveller in the past, but ST:A is a far better system for the purpose.