60cm doesn't say much. Different brands can vary as much as 4cm and all be called a 60cm. Your 60cm might be some other brand's 56.

What define the vertical size od the bike is the head tube length, with the headset. From that, you can determine the absolute minimum bar height.

Your inseam is only 4cm greater than mine and a ride a 51cm LOOK. LOOK frames are sized relatively close to classic models measured center to center.

I'd say it's too big, but maybe not if it's a Trek. Trek's are vertically the smallest for a given frame size, except for the new models that have a 30mm taller head tube.