Everything looks good. The CPU Temp in your bios isn't the actual cpu temperature. That reading is from a sensor located in the cpu socket on the mobo, directly below the cpu. The actual senors for the cpu's "core" temperatures are located in the cpu itself. So with that said, either your cpu is bad or the heatsink is bad or your just using to much paste.
I hate to sound like a broken record, but I would remove the heatsink and clean the cpu and heatsink with rubbing alcohol and a soft, lint free cloth. Let it dry a few minutes. Now throw the Arctic Silver 5 in the trash and get your other paste, the cheap stuff. Put a small gob of the paste in the very center of the cpu. When I say a small gob I mean small, very little, 1/2 the size of a BB, or about the size of a paper match head or 1/2 of a single grain of dried rice. Don't Spread the Paste. I repeat, Don't Spread the Paste. Attach the heatsink (clean, with no paste on the heatsink), the weight of the heatsink will spread the paste for you. Make sure all (4) of the heatsinks locking tabs are securely fastened. Plug the fan in and see what happens.
If your temperatures are still bad I would contact the store you bought the cpu from and request an RMA, or if it's been more than 30 days I would contact Intel and request an RMA. And when you send the cpu back include the heatsink as you'll want a new one of those also.