6+6^2÷9-5

Put parentheses around 9-5 making it (9-5)

                 6+6^2÷(9-5)

Follow the "PE(MD)(AS)" order of operations:

Do the parentheses (9-5) = 4 first and replace (9-5) by 4:

                 6+6^2÷4

Do the exponent 6^2 = 36 second and replace 6^2 by 36:

                 6+36÷4

Do the division 36÷4 = 9 third and replace 36÷4 by 9:

                 6+9

Do the addition 6+9 = 15 fourth (last) and replace the 6+9 by 15:

                 15

That's it.

Edwin