To be continuous, the limits from both sides must be equal so the limit exists, and the limit must equal the value of the function.
Check where the function changes. Each part of the piecewise is continuous, so the only discontinuities are where the function changes.
At -7 the limit from the left is 6 - -7 = 13. The limit from the right is 25. The limit at x = 07 does not exist. There's a discontinuity at x = -7.
Limit from the left at x=5 is 25. Limit from the right is 5^2 = 25. The function value f(5) = 5^2 = 25. The limit exists. It is equal to the function's value. So there is no discontinuity at x=5.
