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.
Workhorse: FX-8320, 24 gigs RAM, Geforce GTX 970, Xubuntu 16.04 x64
Plaything: i5 6600K, 16 gigs RAM, Radeon 7970, Windows 10 x64
HTPC: i3 4170, 8 gigs RAM, Radeon R7 370, Windows 8.1 x64
Wait what: i3 2120, 8 gigs RAM, $GPU, Windows 10 x64