Your computer is not going to shut down because teh cpu temps are 50-60c..........you have some other issue. AS5 is junk imo, and it takes a minimum 100hrs to cure before you know if it helped, and even then you probably looking at a max of 2c difference from the stock thermal paste regarless which brand you choose.
I recommend TX2, 3 or 4, whichever you can find.
http://www.newegg.com/Product/Product.aspx?Item=N82E16835154003
I think your barking up the wrong tree, the temps depend mosly on the ambient room temp, and your case cooling.
Putting the pc on the floor can help because it's cooler. Out of a cabinet if it's in one. Cleaning your fans/filters/heatsinks will help. Adding exhuast fan's will also help a lot.
Either way 50-60c will not cause your computer to shut down. Bios temps are always higher than desktop temps because the cpu runs full speed in the bios, at desktop it clocks down to save power.
Use Hardware Monitor to see what temps your pc is running, it will record the min and max temps while you have it open no matter what tasks your doing.
Hope this helps.