If that's a quality PSU, then 500W is more than enough. I think it's okay at best from the picture. There's no brand or specs to be seen. If it even has a PCI Express 6 pin cable, it will probably work. I would recommend a quality PSU but I suspect your budget is limited.
Your sys with a 7770 will pull less than 300w, so 500w is more than sufficient.
However, as prev mentioned, that PSU may or may not be able
to deliver 500w. Those PSU's (extreme gear i think) are not
known to be of good quality.
I suggest you do your 7770 upgrade with your current psu and
see how it performs. If you pull that psu out now, it will most
likely void the warranty of your system.
I'd be saving up to replace the psu down the line.
CyberpowerPC used the APEVIA TURBOLINK ATX-TL500W-BK as the base 500 Watt PSU model in the Gamer Ultra 2098.
Hardware Secrets did a review on the 450 Watt version of that PSU, the Apevia Turbolink ATX-TL450W-BK, and found that it could only deliver 240 Watts. What they also found was that the Noise and Ripple levels always exceeded the maximum allowed by the ATX12V specifications. That means that the electrolytic capacitors in your system are being destroyed by the out of spec ripple levels.
Thanks to ko888 I eventually found a review by Legit Reviews of this PC. Here's what they have to say:
"The system is powered by a 500 Watt Turbolink branded switching power supply with model number ATX-TL500W-BK. This is a brand that we haven't heard of before. It has two +12V rails with +12v1 being rated at 16 Amps and +12v2 being rated at 18 Amps. This power supply doesn't have any PCIe 6-pin power connectors for video card expansion, which is a bit of a bummer as we always like PCs to have an upgrade path. We took a look around the system and found all the power connectors were used except for one 4-pin molex connector and a SATA power connector." http://www.legitreviews.com/article/1762/4/