The beginning is correct.
To continue, you can remember that something squared is always > 0.
So (x+5)²+13 has a minimum when (x+5)² = 0, because 0 is the minimal value for a square.
For b), (x+5)²+13>22 <=> (x+5)²>9=3²
Write in the form where the values of b and c are to be found.
(a) State the minimum value of and the value of for which this occurs.
(b) Determine the values of for which .
What to do next?