1. **State the problem:** Expand and simplify the expression $ (h + 6)(5 - h) $. 2. **Recall the distributive property:** To expand, multiply each term in the first parenthesis by each term in the second parenthesis. 3. **Apply the distributive property:** $$ (h + 6)(5 - h) = h \times 5 + h \times (-h) + 6 \times 5 + 6 \times (-h) $$ 4. **Calculate each product:** $$ = 5h - h^2 + 30 - 6h $$ 5. **Combine like terms:** $$ 5h - 6h = \cancel{5h} - \cancel{6h} = -h $$ 6. **Write the simplified expression:** $$ -h^2 - h + 30 $$ **Final answer:** $-h^2 - h + 30$