Overclocking an I5-4690K on a Corsair CX500?

Would that be a good idea? I know Corsair PSUs aren't the best in the world. Should I trust it to run an overclocked 4690k, a z97 board, and a GTX 970?

Theoretically yes you could. I've seen people using years old 450 and 500 watt power supplies and really lean on their cpu as far as an overclock. But those power supplies were usually top rated seasonic or super flower variants. From personal experience perfect of having a cx750m just up and die on me when It was running a very mildly clocked fx6300 and two stock gtx 670s, I'd advise against overclocking on that power supply.

Yes, absolutely. You can easily do it. Unless there is something wrong with the psu, it will handle it. Cx series isn't great, but it will put out it's rated power.

Think about it... 970 is a 165w card. The cpu, 88w. Overclock them both and you may be lucky to go over 325w.