Help solving $5^{-4} \left(\frac{2x+5}{8}\right)^2 = 49$ I am trying to solve a simple formula but I get lost in the orders of operation.

The formula is: 

$5^{ -4}{ \left( \frac { 2x+5 }{ 8 }  \right)  }^{ 2 } =49$

The easy parts: 
  $5^{-4} = 0.0016$
  $\sqrt { 49 }  = 7$

So that gives me:

$-0.0016(2x+5/8) = 7$

Am I now allowed to to divide both sides of the equal sign with X to get:

$-0.0016(2+5/8) = 7/x$

?

And if that is correct, then the order of operation is as follows, right?

$-0.0016((2/8)+5) = 7/x$

Am I messing it up completely? :)
So, walking through this step-by-step, in case someone finds this question in the future and needs a more detailed answer, we have

$$5^{-4}\left(\frac{2x+5}{8}\right)^2 = 49.$$

Now, our order of operations tells us to take care of "parenthesis" first. However the expression inside the parenthesis is about as simple as it can get, so we'll leave that alone, for now, and instead take of the exponents. As you calculated, $5^{-4} = 0.0016$, so we have

$$0.0016\left(\frac{2x +5}{8}\right)^2 = 49.$$

We still have an exponent that we would like to get rid of. We can do so by taking the square root of both side, as you did in your attempt, but making sure to square root everything on both sides. This gives us:

$$\sqrt{0.0016 \left(\frac{2x+5}{8}\right)^2} = \sqrt{49}$$
$$\sqrt{0.0016}\left(\frac{2x + 5}{8}\right) = \sqrt{49}.$$

Now, we'll divide each side of our equation by $\sqrt{0.0016}$, and we have

$$\frac{2x + 5}{8} = \frac{\sqrt{49}}{\sqrt{0.0016}} = \sqrt{\frac{49}{0.0016}},$$

The right hand side of this equation is either $175$, or $-175$. So, we have

$$\frac{2x+5}{8} = 175 \ \ \ \text{ or } \ \ \ \frac{2x+5}{8} = -175,$$

and these expressions give us

$$2x + 5 = 1400 \ \ \ \text{ or } \ \ \ 2x + 5 = -1400$$

$$2x = 1395 \ \ \ \text{ or } \ \ \ 2x = -1405$$

$$x =697.5 \ \ \ \text{ or } \ \ \ x = -702.5$$
I would have opted for immediately taking the square root of both sides, if just to simplify the numbers!  $\sqrt{5^{-4}\left(\frac{2x+ 5}{8}\right)^2}= \sqrt{49}$ or $5^{-2}\left(\frac{2x+ 5}{8}\right)= 7$.  Multiplying on both sides by $5^2= 25$, $\frac{2x+ 5}{8}= 175$.  Multiply on both sides by 8, $2x+ 5= 1400$.  I let you do the rest!