1. **Problem statement:** We have a large regular pentagon with side length $x$ and diagonal length $y$. After drawing all diagonals, a smaller pentagon is formed inside. We want to find the side length of this smaller pentagon in terms of $x$ and $y$. 2. **Key properties:** In a regular pentagon, the ratio of the diagonal to the side is the golden ratio $\phi = \frac{1+\sqrt{5}}{2}$. Thus, $y = \phi x$. 3. **Formula for the smaller pentagon's side:** The smaller pentagon formed inside by the diagonals is also regular, and its side length $s$ relates to $x$ and $y$ by the formula: $$s = y - x$$ This comes from the fact that the smaller pentagon's side is the segment between two intersection points of diagonals, which equals the difference between the diagonal and side lengths of the large pentagon. 4. **Expressing $s$ in terms of $x$ and $y$:** $$s = y - x$$ 5. **If desired, express $s$ purely in terms of $x$ using $y = \phi x$:** $$s = (\phi - 1) x$$ where $\phi = \frac{1+\sqrt{5}}{2}$. **Final answer:** $$\boxed{s = y - x}$$