It certainly does not have "500W" - and the brand itself isn't the issue. Chieftec have Delta, CWT and Sirfa units among their product stack (alongside other OEMs, I'm sure). The quality varies dramatically.
The gps-500a8 specifically is based on a very budget platform - a cut down version of the platform that can be found in Corsair's CX or VS lineup (don't remember which... might be both). Neither of those platforms review anywhere close to "good", so a cutdown version of it using poorer quality caps is almost certainly not "fine".
An R9 380X needs at least 28A on the 12V rail.
This unit, supposedly has 34A on the 12V Rail. Ie 408W where it actually matters.
Now, while technically sufficient.... PSUs degrade over time. Typically more rapidly in 'budget' units. I'd be very surprised if that PSU isn't showing degradation barely outside the warrant period, which is 24months:
http://www.chieftec.eu/de/netzteile/ps2/smart-serie/gps-500a8.html
Not a great sign. Not a guarantee it'll fail dramatically either..... but I wouldn't be betting against it.
As for the GPU, while an upgrade is always welcome... it's a matter of what you expect to achieve, the games you play and the resolution.
An R9 380X sits somewhere in the middle of 1050TI-1060 territory,..... so you really have to look at a worthwhile 'step' up in performance to justify the upgrade. Moving to a 1060 or RX580, for example, is likely to be pretty disappointing. A 980TI/1070 or Vega56 would be the minimum I'd look to upgrade to.
BUT, If you play at 1080p/60Hz.... those cards may well be overkill, especially when considering a performance/dollar.