>>/81769/
56 should be fine for that. I looked up the geometry chart of that bike and its not particularly aggressive, I wouldn't worry much about the handlebar height being too low and even if it is there are quick and relatively cheap fixes for that. 
What I'm uncertain about is the seatpost situation and how much you can adjust that. Idk anything about trek bikes but this looks like the seat post is shoved onto the seat tube (opposite of whats the norm) and maybe if the seat tube was cut or is not particularly long in the first place you might not be able to get your desired seat height. I recommend checking that out for sure