The grease never dries up so cleaning it is a cinch. I always use alcohol to clean my CPU and heatsink when I do make changes to the heatsink and fan. Wipe it down real good. Then, don't touch the part you cleaned anymore. Your fingers have grease without you even knowing about it.
Once it is cleaned off, make sure there are no lint or any kind of small stuff around it. Actual application of the Arctic Silver 5 take no more than 5 seconds. A small dab in the middle and that's it. I usually lay the CPU in the socket first before I apply, but whatever works for you. Then just lay that big heatsink on it.