1. **Problem statement:** Find the value of $x$ for the parallelogram where one side is $5x + 10$ and the opposite side is $130$. 2. **Formula and rule:** Opposite sides of a parallelogram are equal, so: $$5x + 10 = 130$$ 3. **Solve for $x$:** $$5x = 130 - 10$$ $$5x = 120$$ $$x = \frac{120}{5} = 24$$ 4. **Final answer:** \boxed{24}