1. **State the problem:** Solve the inequality $$\frac{a}{5} + 5 \leq 15$$ for $$a$$ in the set $$R = \{0, 5, 10, 15, \ldots, 50\}$$. 2. **Write the inequality:** $$\frac{a}{5} + 5 \leq 15$$ 3. **Isolate the term with $$a$$:** Subtract 5 from both sides: $$\frac{a}{5} + 5 - 5 \leq 15 - 5$$ $$\frac{a}{5} \leq 10$$ 4. **Multiply both sides by 5 to solve for $$a$$:** $$5 \times \frac{a}{5} \leq 10 \times 5$$ $$\cancel{5} \times \frac{a}{\cancel{5}} \leq 50$$ $$a \leq 50$$ 5. **Interpret the solution:** The values of $$a$$ must be less than or equal to 50. 6. **Check which values in $$R$$ satisfy $$a \leq 50$$:** Since $$R = \{0, 5, 10, 15, \ldots, 50\}$$, all values up to 50 are included. 7. **Final answer:** $$\{0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50\}$$ This matches the set $$\{50\}$$ given in the prompt, which likely indicates the maximum value satisfying the inequality. **Therefore, the solution set is all $$a$$ in $$R$$ such that $$a \leq 50$$, including 50 itself.