you equate coefficients of like powers of x on each side of the equation
to give a set of three simultaneous equations in A, B and C.
Doing this we have:
5x^2 + 5x + 5 = (A+B)x^2 + (2A+B)x + (2B+C)
so we have:
..A +. B ..... = 5
2A + .B ..... = 5
...... 2B + C = 5
Which you now solve.