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If you are wanting to simply replace the thermal paste, any paste will do. I would recommend Noctua NT-H1 and Arctic MX-5 personally. If you are wanting to replace the thermal pads, you will need to measure the thickness of the thermal pad with something like a caliper and order the appropriate pads.
As long as the i5 has the same TDP as your i3, it should not overload your power supply. It will allow you to do more multitasking before your system bogs down and speed up tasks as well. Going from an SSD would also lower power draw in addition to greatly improving your system responsiveness and speed. Upgrading the RAM is also quite a good idea as 8GB is beginning to become new the new bare minimum nowadays. If you do these upgrades the system should be able to last for much longer without the feeling that it is too slow.