Your PC wont even boot with new and stronger PSU due to i5 not having integrated GPU inside, while i3 has it. Meaning you need to buy new GPU. Here is a list with some low consumption GPU from recent test i stumbled upon:
Test.
Test on that image was conducted using i5 2500k, 4gb ddr3, asus p8p67-m pro and wd black 1tb.
My thoughts on PSU, if its not good brand: seasoneic, antec, xfx, fortron (fcs elite group), Get a new one. Anything above 200w from brands mentioned should do the trick. If you plan on upgrading to a stronger GPU, get something along the lines of seasonic 430 or xfx 450.