Since $7$ oranges weigh the same as $5$ apples, we can set up a proportion to find the number of apples Jimmy would need.
The proportion is $\frac{7 \text{ oranges}}{5 \text{ apples}} = \frac{28 \text{ oranges}}{x \text{ apples}}$, where $x$ represents the number of apples needed.
Cross-multiplying, we get $7x = 5 \cdot 28$, which simplifies to $7x = 140$.
Dividing both sides by $7$, we find that $x = \boxed{20}$.
Therefore, Jimmy would need $20$ apples to equal the weight of his $28$ oranges.The answer is: 20
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Jimmy notices $7$ oranges weigh the same as $5$ apples.  If Jimmy has $28$ oranges, how many apples would Jimmy need to equal the weight of his $28$ oranges?

### Answer:
