I have a 2yo Percheron/paint cross gelding and right now he's standing at about 15.2hh...and growing. He is going through a growth spurt right now, in fact. We've already been through two halters (I finally gave in and ordered him a custom-made rope halter), and had to replace the throatlatch on his bridle. By next month, I expect to have to buy him a new bit because the 5" french link we're using right now is just on the verge of being too small for him. Oh, and did I mention that I've only had him for two months?! LOL!
I did the string test on Aires and he's going to top out around 17hh, maybe a little taller (his dam was a 17.3hh Percheron and his sire was a 15.1hh APHA stud).
This is a conformation shot of Aires I took a couple of weeks back. He's starting to get more uphill now (he was EXTREMELY downhill when I bought him). For reference, the hitching rail he's tied to is about hip-height on me.
Oh, and I'm 5'7" as well and Aires looks just about the same standing next to me as your boy looks standing next to you (maybe a wee bit shorter, but not by much).