Five numbers in A.P.: (a-2d,\ a-d,\ a,\ a+d,\ a+2d)

Sum: (5a=25\implies a=5)

Sum of squares: [ 2[(5-2d)^2+(5-d)^2]+25=135 ] [ (25-20d+4d^2)+(25-10d+d^2)=55 ] [ 50-30d+5d^2=55 ] [ 5d^2-30d-5=0 ] [ d^2-6d-1=0 ] Wait recalculate with (4a^2+10d^2) style:

Sum of squares = (5a^2+10d^2=135) [ 5\cdot25+10d^2=135\implies125+10d^2=135\implies d^2=1\implies d=\pm1 ]

Numbers: (3,4,5,6,7)

Answer: (3,4,5,6,7)