I am solving for X below:
4^{3x+5 }= 1/256
The answer I get is -3 please correct me if I am wrong and why if you can please. Much appreciated.
Well as it's written we can't tell if you meant $\displaystyle \displaystyle \begin{align*} 4^{3x + 5} = \frac{1}{256} \end{align*}$ or $\displaystyle \displaystyle \begin{align*} 4^{3x} + 5 = \frac{1}{256} \end{align*}$ or even $\displaystyle \displaystyle \begin{align*} 4^3\,x + 5= \frac{1}{256} \end{align*}$. Simply by putting what you meant to have as the power in brackets can overcome this ambiguity.
Surely you know that $\displaystyle \displaystyle \begin{align*} \frac{1}{256} = \frac{1}{4^4} = 4^{-4} \end{align*}$.
So if $\displaystyle \displaystyle \begin{align*} 4^{3x+5} = 4^{-4} \end{align*}$ what do you think the next step should be?