Notre Dame. He may have grown but let's assume he hasn't.
Drew Brees is 6' 0"
Aaron Rodgers is 6' 2"
Tony Romo is 6' 2"
Matthew Stafford is 6' 2"
Michael Vick is 6' 0"
Russell Wilson is 5' 11"
...and just think Golson doesn't even have to run an NFL team. Golson tends to throw in a 3/4 arm slot. The coaches will probably work on getting his wrist over his elbow on passes over the middle that should help with getting over the line...that said height in a spread QB (unless he's really short) isn't as much of a factor as pocket speed, arm strength, elusiveness, touch.