Intel stock paste isn't bad, but like some others it does dry out. This normally isn't an issue as it's what's in the paste that makes thermal conductivity possible, the paste itself just being the medium to hold that stuff. Problems arise when the paste is dried out and suffers shock of some sort, can be as simple as a vibrating fan or a bump while cleaning. This shock can break the seal of the paste, so you don't get a good transference of heat, and temps go way up.
Solution is buy a decent paste, (not AS5) like arctic MX4 or Noctua or Grizzly as those don't dry out and will last longer than the cpu.
An alternate solution, which is the better value overall, is replace the stock Intel cooler with a decent aftermarket cooler. Cryorig...