To solve this equation, let's first simplify the expression by combining like terms:

5^$x$ + 5^$x+1$ + 5^$x+2$ = 3^$x$ + 3^$x+1$ + 3^$x+1$

Rearranging the terms on the right-hand side:

5^$x$ + 5$5^{(}x)$ + 5^2$5^{(}x)$ = 3^$x$ + 3$3^{(}x)$ + 3$3^{(}x)$

Now, we can simplify further:

5^$x$ + 5$5^{(}x)$ + 25$5^{(}x)$ = 3^$x$ + 3$3^{(}x)$ + 3$3^{(}x)$

5^$x$ + 5$1+5+25$ = 3^$x$ + 3$1+3+3$

5^$x$ + 5$31$ = 3^$x$ + 3$7$

5^$x$ + 155 = 3^$x$ + 21

Now, we can isolate one of the variables, let's isolate x on the left side of the equation:

5^$x$ - 3^$x$ = 21 - 155

Now we can attempt to simplify by making x the subject of the formula, do you have any preference on how we go about solving this part or do you have any specific instructions for simplifying this equation further?