Your new card takes a good 4-5 times the power of the current one. I have used the same power supply with light cards(think 4350, and you dont want to game on that).
I would put you very close for that unit. It only delivers about 170 watts of 12 volt power.
Your card of choice will take off about 40(games only 10 at idle) of that and up to 60 at high load.
The cpu is rated at 65 watts. While I bet it takes less(and much less at idle). You see what is happening right? we are getting upwards to the end of what that power supply will deliver.
I run some pretty close limits systems(or some would say), but even i would be a bit worried about it.
The big issue here is that the power supply is question does not deliver much 12 volt power(about 170 watts). With even 200, it would generally be in range of being safe for your system.
AMD's recommendation of a 400 watt power supply honestly assumes a real bad power supply and fully loaded system.
I personally run an
H55N USB3 mini itx
i5 750 - undervolted
1TB drive - Western Digital Blue
2 sticks of ddr3 @ 1.65 volts
AMD 5770
(needs a 450 watt power supply)
SlimDVD
All off a little 300 watt power supply(22 Amps or 264 watts of 12 volt) and never even push 200 watts from the wall. Games average 140-170. I built this system around the power supply limit not the other way around.
But i have a hard time recommending you do this because, your system may just be too much for that power supply.
Bottom line. Even I think a new power supply is in order. A good quality 300(like something from seasonic) will run the system without working too hard, but you should go a bit higher for longer lasting system/power supply.
Remember, the 12 volt rail(s) are the most important thing in a modern power supply and you can not just add all together when there is more then one. There is generally a listed max combined. Not all 250 watt power supplies are created the same