Currently my front chainrings are Shimano FC-5600 48/40 with FD-5600 derailleur. As I can not get new chainrings in FC-5600 I was asking myself if my FD-5600 supports FC-5700 53/39 chainrings?
The FD-5600 derailleur has capacity of 16 tooth difference between the rings so it will be fine with 53/39. You will need to move it up on the frame to accommodate the bigger rings of course.
If your bike was designed for smaller rings check you have enough clearance between the rings and chain stays.
As there is a larger difference between the rings also check that you will not exceed the total capacity of your rear derailleur. Total capacity is (large ring-small ring) + (largest sprocket-smallest sprocket).
I’m not sure if 105 5700 rings will actually fit on a 5600 crank. They both have evenly spaced 5 bolt spiders, but the shape of the rings where they meet the crank body might be different.
Shimano’s archived specs for 2006/2007 when 105 5600 came out are here