Find $x$, if:

$\dfrac{25^x \times 5^5 \times (125)^3}{5 \times (625)^4} = 125$

$\dfrac{25^x \times 5^5 \times (125)^3}{5 \times (625)^4} = 125\\[1em] \Rightarrow \dfrac{5^{2x} \times 5^5 \times (5^3)^3}{5 \times (5^4)^4} = 5^3\\[1em] \Rightarrow \dfrac{5^{2x} \times 5^5 \times (5)^9}{5 \times (5)^{16}} = 5^3\\[1em] \Rightarrow \dfrac{5^{2x+5+9}}{5^{1+16}} = 5^3\\[1em] \Rightarrow \dfrac{5^{2x+14}}{5^{17}} = 5^3\\[1em] \Rightarrow 5^{2x+14-17} = 5^3\\[1em] \Rightarrow 5^{2x-3} = 5^3\\[1em] \Rightarrow 2x - 3 = 3\\[1em] \Rightarrow 2x = 3 + 3\\[1em] \Rightarrow 2x = 6\\[1em] \Rightarrow x = \dfrac{6}{2}\\[1em] \Rightarrow x = 3$

If $\dfrac{25^x \times 5^5 \times (125)^3}{5 \times (625)^4} = 125$, then $x = 3$.