Why not go and code something, and we will help with any problems.
Hint: if all you are doing is summing a 5x5 matrix, you probably dont want a 5x5 matrix in VHDL (because each element arrives serially, you can sum them in the time domain).
send the data as a raster scan. I assume your input from pc through UART should be an image. So send the pixel data from top left to bottom right through UART port in a raster fashion i.e first pixel and then second pixel serially. Your receiver system on the fpga side should also be the same.