You should be fine. That CPU has a TDP of 95w, the 4790 with a TDP 84w works fine with a 300w PSU in a fairly basic PC. But a 300w PSU is not very powerful. If you have plans to upgrade your video card you will probably need a more capable PSU as soon as you think about graphics.
But unless you are getting that Intel i5 2380P for next to nothing, I'm not sure it is a wise upgrade. There are more efficient CPUs that are both more powerful and use less electricity. Also the real world performance from the above named CPUS would not be that much of a difference. slightly Faster per-core dual-core vs slightly slower per-core quad core. You would probably be happier saving a little longer for a newer PC.