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e^(i*pi) There are no real solutions because $\displaystyle 5^(x-2) \geq 0 \: , \: x \in \mathbb{R}$
In the complex plane the principle solution of $\displaystyle \ln(-1) \text{ is } i\pi$ (this follows from Euler's indentity - which happens to be my username)
$\displaystyle (x-2)\ln(5) > i\pi$
$\displaystyle x > \dfrac{2}{\ln(5)}+\dfrac{\pi}{\ln(5)}\,i$