1. **State the problem:** Solve the simultaneous equations: $$5p - 3q = 16$$ $$p - 39 = -4$$ 2. **Rewrite the second equation:** $$p - 39 = -4$$ Add 39 to both sides: $$p - 39 + 39 = -4 + 39$$ $$p = 35$$ 3. **Substitute $p = 35$ into the first equation:** $$5(35) - 3q = 16$$ Simplify: $$175 - 3q = 16$$ 4. **Isolate $q$:** Subtract 175 from both sides: $$175 - 3q - 175 = 16 - 175$$ $$-3q = -159$$ Divide both sides by $-3$: $$\cancel{-3}q / \cancel{-3} = \frac{-159}{-3}$$ $$q = 53$$ 5. **Final answer:** $$p = 35, \quad q = 53$$