will my psu run to gpu r7 250 gddr5 my psu is powerlogic atx 550w

Solution
That psu pushes a miserly 12amps on the 12v rail. That said, if your r7-250 is of the style that has no added 6pin power requirements, then yes, your psu will work, as power is drawn directly from the pcie slot and the card only pulls 65w. Your psu has @140w 12+. This will max out your options as you will need 12v for other sources on the motherboard and such things as fans and hdd and optical drives.
Sorry, but you have a sub-standard psu. Most 550w units are capable of @36a or better on 12v

Karadjgne

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That psu pushes a miserly 12amps on the 12v rail. That said, if your r7-250 is of the style that has no added 6pin power requirements, then yes, your psu will work, as power is drawn directly from the pcie slot and the card only pulls 65w. Your psu has @140w 12+. This will max out your options as you will need 12v for other sources on the motherboard and such things as fans and hdd and optical drives.
Sorry, but you have a sub-standard psu. Most 550w units are capable of @36a or better on 12v
 
Solution

Karadjgne

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Your cpu doesn't have much bearing on if you can run that gpu. What does is your motherboard. AMD gpus are backwards compatible upto a point. You can use pcie3 on a pcie2.2 or later board. Prior versions used a different power architecture, so are unlikely to be compatible. For instance, if your motherboard is pcie 2.0, it may not work, if your motherboard is pcie 2.2 it should. If your motherboard is 2.0, youll probably have to search for an older generation gpu which would be compatible.
Nvidia gpus are fully backwards compatible from 3.0 to 1.1, so that may be an option, with your psu I'd suggest the gtx 750.