1. The problem states that the ratio (common ratio) of a geometric progression (G.P.) is given as $\frac{25}{49}$. We have the second term as $x + 5$. 2. Let's denote the first term of the G.P. by $a$ and the common ratio by $r = \frac{25}{49}$. 3. The second term of the G.P. is given by $ar$. Therefore, $ar = x + 5$. 4. To find $x$, we rearrange to get $x = ar - 5$. 5. The problem is ambiguous regarding the first term $a$, so if we assume $a = 1$ (which is common for finding $x$), then: $$x = \frac{25}{49} - 5$$ 6. Calculate $x$: $$x = \frac{25}{49} - \frac{245}{49} = \frac{25 - 245}{49} = \frac{-220}{49}$$ 7. Thus, the value of $x = -\frac{220}{49}$. If another value of $a$ is given, $x$ will depend on it accordingly.