This simplifies to $$\frac{6}{5} \times \cdots \times \frac{2025}{2024} = \frac{2025}{5} = 405.$$

(1 + 1/5)(1+ 1/6)(1+ 1/7)...(1+1/2023)(1+1/2024) =(6/5)(7/6)(8/7)...(2024/2023)(2025/2024) = 2025/5=405. The answer is 405.

$$\prod\limits_{k=5}^{2024}(1+\frac{1}{k})=\prod\limits_{k=5}^{2024}(\frac{k+1}{k})=\frac{2024+1}{5}=405$$

We can express this as $\frac{6}{5}\times\frac{7}{6}\times\frac{8}{7}\times...\times\frac{2024}{2023}\times\frac{2025}{2024}$. Observe that this is a telescoping series, which means that the $6$ and $6$, $7$ and $7$,...,$2024$ and $2024$ in adjacent terms cancel out. This leaves us with $\frac{2025}{5}$, which is just $\boxed{405}$.