Assuming that the i5 enjoys a 40% linear per-clock improvement over the Core 2, a handy back of the envelope calculation indicates the i5 2500k at stock would be (3300 *1.4 = ~4.62 GHz) in terms of an effective speed comparison relative to what you have now, assuming that its new instruction set support doesn't come into play. A speed boost of 35% isn't trivial, but given current requirements in games the 4870 is likely your bigger bottleneck. At that high a clock speed I'm hard-pressed to imagine a Core 2 Quad seriously bottlenecking your GPU in a way you'd really notice. More to the point, the 4870's ongoing driver support was recently dropped, and it will not improve with time. Snag the 7870; in the event that proves insufficient, THEN start saving your pennies.
Dead Man Walking: i5 6600K, 16 gigs RAM, Radeon RX 480, Windows 10 Pro x64
Endpoint: Ryzen 7 1700, 16 gigs DDR4-2400, Radeon RX 480, Win10 Pro x64 / Xubuntu 17.04
HTPC: i3 4170, 8 gigs RAM, Geforce GTX 1050 Ti, Windows 8.1 x64