Looks like you've got an intermittent short between 5V and chassis ground. (Plus a power supply that doesn't shut down the 5V rail even when a dangerous current is flowing down it.)

Where the short is (somewhere on your motherboard, or on something powered via your motherboard, perhaps USB or a fan), you should see similar overheating damage to that on your power connector. It probably also smells faintly of smoke. Your computer is a fire risk until you find and fix the short.

You're relatively lucky: I had a PC once short 5V to 12V, which had the effect of blowing the motherboard, the CPU, all the expansion cards, all the hard drives, the CDROM, and the tapestreamer. Fortunately the PSU shut down before anything caught fire, or even got as blackened as your connector.

Peter