Yes its good enough.
I still feel like the Ivy bridge 3570K is a good enough CPU (Its still the CPU in my primary computer), it might be four years old now, but its still quite fast even without an overclock. Your PSU is probably going to be okay, its from a reputable brand, and is decent wattage. Upgrading to an i5 6500 probably wouldn't gain you too much if you are looking to save money, as you can simply overclock your i5 3570K to match the 6500's performance (note that the 6500 is NOT unlocked). H77 unfortunately does not allow for overclocking. If you want to overclock your 3570K, you will need to get a P67/Z68/Z75/Z77 (I recommend Z77) motherboard, which allows for adjustment of the multiplier. Since your CPU has a PCIe 3 controller in it, you should get a motherboard that supports PCIe 3. Anyway, since you asked if you can replace as few parts as possible, the GTX 1080 will drop right in and work fine. Overclocking was just a suggestion since you mentioned the i5 6500 processor.