This 500W psu came with a prebuild PC

Solution
the simple answer is no.
It's a super basic and cheap PSU.
It's not even 80+ rated as far as I can tell.

You first need to get a better PSU for it.

If on a serious budget then this is the best PSU I can recommend that won't explode.
(I mean, you could pair a 780/970 with it since it is a 500w PSU, but it's a trash PSU so I would highly recommend against using it with a GPU)

https://pcpartpicker.com/product/TgW9TW/seasonic-power-supply-m12ii520bronze

costs $55 on Newegg and if you take advantage of the mail in rebate, you'll get $20 of it back in the mail.

Otherwise, the current PSU you have just according to it's label has enough wattage to power the GPU and your system. And you can use it if you want, but you do so at your own risk.
the simple answer is no.
It's a super basic and cheap PSU.
It's not even 80+ rated as far as I can tell.

You first need to get a better PSU for it.

If on a serious budget then this is the best PSU I can recommend that won't explode.
(I mean, you could pair a 780/970 with it since it is a 500w PSU, but it's a trash PSU so I would highly recommend against using it with a GPU)

https://pcpartpicker.com/product/TgW9TW/seasonic-power-supply-m12ii520bronze

costs $55 on Newegg and if you take advantage of the mail in rebate, you'll get $20 of it back in the mail.

Otherwise, the current PSU you have just according to it's label has enough wattage to power the GPU and your system. And you can use it if you want, but you do so at your own risk.
 
Solution
no clue about the quality of that psu. but i would think it would support a 970 pretty easily. they only run about 150w or so if you don't try to run a super oc'ed version. you can get similar performance out of a newer 1050ti card and they use less than 100w. no idea what pricing is like for them but i'd look at newer more efficient cards first. then settle for a 970 if you can't get anything else.

the 780 uses WAY more power and i'd not trust one to that unknown psu. they start at 250w and go up from there!!!

best case is to get a new psu that is known to be a quality unit.