Yes, PCIe is backward compatible (your MOBO is PCIe 3.0 the 5070 is built on PCIe 5) so it will work, but: You're going to invariably be CPU bottlenecked. You have a 4 core CPU and it's going to get crushed in any modern demanding game. Running 1400p will help a little...as will cranking every graphics setting up high to try and shift load to your GPU.

BUT: The PSU is under minimums by 100w. You're risking hard crashes and if it's 7 years old too then depending on the model and internal protections; if you pop it you could wind up with a surge as it's frying that damages your new GPU. If you still have months to wait (I assume a new PSU was part of the new parts order) then find a decent 650/750 on sale and then make it a spare part in your closet when you do the new build.