Hi and welcome.
Borderline it should fit that case from what I can find it will manage up to a 339mm card length. Power wise it might work, but it also might not last long.
CPU is not using much more than 100W and then it really depends on the exact model of Vega 56 you are talking about. The AMD reference card only pulls around 250 W, but some of the overclocked cards from AIBs (Powercolor etc) can go some way north of 300W in very demanding games which would make me nervous with that PSU.
Although it says its a 500W model it only goes up to 456W on 12V, which is what the CPU and graphics card are using. If you hit a game that maxes both CPU and GPU you could be bouncing off that maximum capacity. You could see shutdowns, if youre lucky and it doesnt pop and take something else in the system with it instead.
Also take into account the PSU only has a 3 year warranty which I assume it passed, and it wasnt the best quality to begin with.
TLDR I advise against it. Something like a GTX 1080 would be safer, but like I say the PSU is old and is advisable to replace asap.