Cannot find some parameters details for this board
The current will probably be limited by the traces on the board. See the schematics of the development board: Schematics
Full documentation is found here, which can be useful to read: Documents
On sheet 4/14 you will find that the 5V rail is just connected to your 5V input via a jumper. Here is the relevant portion:

E5V stands for your external power source. If your source can support your required load plus the discovery board itself, there should be no problem.