Do I have a bad power supply?

[HiImAyumi]

Recently, my PC would shut down with no warning, not even a reboot just powers down. i thought my CPU was over heating so i got some thermal paste from the store, cleaned off the old paste and applied a new coat the size of a grain of rice and spread it around,
when playing PSO my CPU would get up to roughly 120F which isn't bad.
however even after applying the new paste my pc would turn off still, i tested my RAM with taking out one stick at a time and still does it.
if it's not my CPU or RAM i would guess my power supply is taking a turn for the worse. Is my assumption correct.?

[Rain Walker]

Yes

5psu