No. The CX 500 hasn't been made in a decade. A mediocre PSU that is a decade old is a no go. Only the CX PSUs with black-and-white labels, the ones they started making in 2014, are good budget PSUs. And even if we pretend the green-label ones were good, they're a decade old now.
Unfortunately, you're hamstrung by your decision to get an RX 570. You had no business buying a GPU that required supplementary power unless your PSU situation had been taken care of. This was like buying a sports car but not having enough money for the car insurance; if you don't have enough money for the insurance, you don't really have enough for the car. You could easily have gotten a GTX 1050 Ti or a GT 1030 or a GT 750 Ti that would have been safer on lower quality PSUs like the ones you're looking to buy. But you didn't.
You can run the GPU on anything you like, it's your money and your risk. But running on ancient PSUs of middling-at-best quality maximizes the chances that your RX 570 (and the rest of your PC) does not live very long. If you want to do something that isn't a good idea, nobody here is going to stop you. But we're going to give you good advice, just like the doctor who will advise you against eating a pound of bacon for breakfast every morning and the HVAC technician who tells you to change the air filter in your furnace regularly.