Ans is base 8. This is the explanation. The coefficients in given eqn are in base b. A quadratic eqn can be represented as x2 - (sum of roots) + product of roots. Therefore here sum of roots is 13(in base b) and product of roots is 36(in base b). Now you can represent 13 in base 10 as 1*b^1 + 3*b^0 and 3*b^1+6*b^0 in base 10. Therefore 13 is b+3 in base 10 and 36 is 3b+ 6 in base 10.
From roots as x = 5, 6 we can know one thing that since the roots are still in base b , therefore, the max value (that we know now from current scenario) is that the base is atleast greater than or it might be equal to 7 as for a base b the max value is b-1.
Now the roots are given as x = 5, 6. Therefore we can form the eqn from given roots using sum of roots and product of roots. The eqn is x2 - 11x + 30. Now b+3 = 11 and 3b+ 6 = 30. Solving any of these you will get b = 8 and hence the answer.
You can even try to convert 13 in base 8 to 11 in base 10 and 36 in base 8 to 30 in base 10.