Hello,
Have you considered to upgrade only the GPU now ? In games most work is made by the GPU, and the CPU is there basically to feed information to the GPU. A Phenom II x4 965 BE is really not bad processor, I dare to think it will be enough for most games with a more powerful GPU. I personally have a FX-8350 and GTX 970, but next time I upgrade CPU I will also buy a new motherboard and switch to Intel. As AMD left the processor's market and now produces only APUs, I see no reason to stick with AMD processors.
If I was you I would spend all that money in a good GPU (like a factory overclocked GTX 970) that you can reuse later even if you decide to change motherboard and processor. The 550ti is very low card, I know it, I have one next to me. It belonged to my nephew, I gave him as a gift a second hand GTX 770 and I will sell the 550ti for whatever I can get. Maybe, just maybe, your cpu will become the bottleneck, but you will see huge improvement upgrading just the gpu. Most games use still at most 4 cores, and the 4 cores of your processor are powerful.
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