I've never heard of an Athlon i7. Is this a desktop PC? (sounds like it since you're considering a new HSF)
Follow these steps in order: If the heatsink fan recently started spinning so fast, it's likely NOT the heatsink/fan going bad.
1) Get a can of air and clean out the dust. Heatsink/ Fan/ Everything else.
2) Monitor temps. I use HW Monitor.
If your temps go down to "normal" but the fan rpms don't, the problem isn't the fan, it's the controller. If this is the case, you could try a program called Speed Fan.
Gives you access to temp sensors and fan controls. Think of it as a mobo fan control override.
3) If the temps don't go down at idle with the fan spinning at 5000rpm and the heatsink fins are clean of dust; Re-seat the heatsink. Maybe the TIM dried up.
4) If all else fails, get a new heatsink.
Main: i5-3570K, ASRock Z77 Pro4-M, MSI RX480 8G, 500GB Crucial BX100, 2 TB Samsung EcoGreen F4, 16GB 1600MHz G.Skill @1.25V, EVGA 550-G2, Silverstone PS07B
HTPC: A8-5600K, MSI FM2-A75IA-E53, 4TB Seagate SSHD, 8GB 1866MHz G.Skill, Crosley D-25 Case Mod