Should I purchase a new PSU for R9 280X

Solution
CX500 is an entry level PSU from Corsair, I would change you PSU to this one.

PCPartPicker part list / Price breakdown by merchant / Benchmarks

Power Supply: Antec High Current Gamer 620W 80+ Bronze Certified Semi-Modular ATX Power Supply ($59.99 @ NCIX US)
Total: $59.99
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-04-20 14:48 EDT-0400)

Recommended PSU for 280X is 600W and that CX500W might fail in your system because it has cheap capacitors.
 
Solution