GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
#g4 f2 z1 5x5 0 0 1 0 0 0 0 0 1 0 -1 0 1 0 0 0 -1 0 1 0 0 0 0 0 1 5x5 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 5x5 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 5x5 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 -1 5x5 4 -2 -2 1 0 -2 4 1 -2 0 -2 1 4 -2 0 1 -2 -2 4 0 0 0 0 0 0 5x5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 5x5 0 1 1 1 1 -1 0 1 0 1 0 0 0 1 1 0 0 0 0 1 1 -1 1 1 -1 2^5*3^2 = 288