Is this power supply to old?

Your system shouldn't need more than 400W, but to be safe for future upgrades, I would recommend aiming for a good quality 500W supply.
If you're in a budget and looking for as much quality as possible, I would look at Corsair CXM series ([URL=https://pcpartpicker.com/product/3hkwrH/corsair-power-supply-cp9020102na]Corsair CXM 550 W[/URL]) as well as be quiet! Pure Power 11 500W ([url=https://pcpartpicker.com/product/cTfhP6/be-quiet-pure-power-11-500-w-80-gold-certified-atx-power-supply-bn901]non-modular[/url], [url=https://pcpartpicker.com/product/qpvbt6/be-quiet-pure-power-11-cm-500-w-80-gold-certified-semi-modular-atx-power-supply-bn297]modular[/url]).

if a PSU goes, it can potentially take your whole system with it .. don't skimp on your psu... I'd recommend getting a quality 80+ gold 600w or better that can stick with you through several upgrades. Your rx580 can pull upwards of 300w on it's own when under load. (based on review I just read comparing the RX580 do the new 5600XT).

Any PSU can die at any time and do potential harm to your PC.. but having 1 bullet as opposed to 5 bullets in your six shooter while playing russian roullette .. your playing with 5 bullets.