The Core i3-550 is a Clarkdale processor and it includes a graphics engine. The Core i5-750 is a Lynnfield processor and does not include a graphics engine. If you want to use this particular Core i5 processor, you will need to add a NVIDIA or AMD/ATI graphics card to your system. If you want to get an alternative Core i5 processor that does include a graphics engine, your choices are the i5-640, i5-655K, i5-660, i5-661, i5-670 or i5-680. Here is a comparison of these processors: https://ark.intel.com/content/www/us/en/ark/compare.html?productIds=43550,43553,43556,43546,48504,48750,42915.
Now, as for it overheating, this i likely because you did not provide the proper amount of Thermal Interface Material (TIM, heatsink paste) and/or properly secure the cooling solution (heatsink/fan) to the processor and board.
I would add that the Clarkdale processors' graphics engine is NOT supported on Windows 10. If you want to use a computer this old with Windows 10, you should include an add-in NVIDIA or AMD/ATI graphics card.
Hope this helps,