If $x : y = 5 : 6$, then find the ratio of $(2x + 3y) : (3x + 5y)$.

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**Solution:**

1. Given the ratio $x : y = 5 : 6$, we can write:
   - $x = 5k$
   - $y = 6k$

2. Substitute these values into the expressions:
   - $2x + 3y = 2(5k) + 3(6k) = 10k + 18k = 28k$
   - $3x + 5y = 3(5k) + 5(6k) = 15k + 30k = 45k$

3. Therefore, the ratio is:
   $$ (2x + 3y) : (3x + 5y) = 28k : 45k = 28 : 45 $$

4. Check the options: $28 : 45$ corresponds to option (b).

**Answer:** $28 : 45$

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