To solve this equation, we can start by simplifying both sides.

On the left side, we have √x + 4√x + 4. Combining like terms, we get 5√x + 4.

On the right side, we have 2 + √5.

So now our equation becomes 5√x + 4 = 2 + √5.

Next, let's isolate the square root term on one side of the equation. Subtracting 2 from both sides, we have 5√x + 2 = √5.

Now, let's isolate the square root term by subtracting 2 from both sides: 5√x = √5 - 2.

To get rid of the coefficient of 5 in front of the square root term, we can divide both sides of the equation by 5: √x = (√5 - 2)/5.

Finally, to solve for x, we square both sides of the equation: x = (√5 - 2)^2/25.

Therefore, the solution to the equation is x = (√5 - 2)^2/25.