will my power supply do the trick?

No, get a 600W+ PSU from XFX, Seasonic, or Corsair (TX, HX, and AX series only).

http://www.tomshardware.co.uk/answers/id-1804779/power-supply-unit-tier-list.html
Tier four - Not for overclocking systems or high end gaming rigs. May not even output labeled power and fail standard ATX specifications slightly. May even use cheap components to meet a price


Aerocool
Strike-X series
Templarius Imperator series

Asus Atlas
Cooler Master GX / GX lite series (The GX 450 non-lite Watt model is fine)
E-power units

EVGA
430 / 500 80+
500B / 600B

FSP Raider series
Futurepower
Hiper Type M (Less than 600 Watts)
HIPRO
LC power
Masscool
MGE XE
Mushkin HP series
NorthQ 4775-500S / BU

NZXT
Hale82N 650w
Hale82 V2 700w

OCZ
GameXStream (less than 1000 Watts, if manufactured before December 2007)
GameXStream 1010 Watts (it's an 850 Watt unit in disguise)
ModXStream (if manufactured before December 2007)
Fatal1ty 2013 550 and 750 Watts
StealthXStream (If manifactured before December 2007)

Scythe Kamariki
Superflower Amazon series

Ultra
Xfinity series
U2 X2 series (Less than 700 Watts)
XVS series

Xion Real Power series