Each slot has a maximum memory capacity of 4GB Memory, for a total of 16GB.
The bus interface of the Radeon HD 5970 is PCIe 2.1 x16, and i'm not sure but the motherboards x16 slot is probably PCIe 2.0, so it will work but maybe not at it's maximum speed.
The i5 6300 will not work. That is a 6th Generation Intel processor requiring a different LGA socket.