1. **State the problem:** We need to find the perimeter of a hexagon with side lengths given as 5 inches, 5 inches, 9 inches, 9 inches, 5 inches, and 5 inches. 2. **Recall the formula for perimeter:** The perimeter $P$ of a polygon is the sum of the lengths of all its sides. 3. **List the side lengths:** The hexagon has sides: $5, 5, 9, 9, 5, 5$ inches. 4. **Calculate the perimeter:** $$ P = 5 + 5 + 9 + 9 + 5 + 5 $$ 5. **Simplify the sum:** $$ P = (5 + 5) + (9 + 9) + (5 + 5) = 10 + 18 + 10 = 38 $$ 6. **Conclusion:** The perimeter of the hexagon is $38$ inches.