The processor will not drop onto that board since the sockets/pins are different. The i5-7500 is LGA1151 and the H81 is meant for LGA1150. If you want to keep your pick of the i5-7500, you should be looking at the B250 board. To add, you're also going to need DDR4 ram for the new processor+motherboard.
The GPU will drop onto the board provided the PSU can deliver the power for your entire system.
Speaking of which, can you please pass on your full system's specs like so:
CPU:
Motherboard:
Ram:
SSD/HDD:
GPU:
PSU:
Chassis:
OS: