#### Answer

$\color{blue}{x=5}$

#### Work Step by Step

Add $6$ to both sides to obtain:
$\sqrt{4x+5}=2x-5$
Square both sides to obtain:
$4x+5=(2x-5)^2
\\4x+5=(2x)^2-2(2x)(5)+5^2
\\4x+5=4x^2-20x+25$
Move all terms to the left side of the equation.
Note that when a term is transferred to the other side of the equation, its sign changes to its opposite.
$0=4x^2-20x+25-4x-5
\\0=4x^2-24x+20
\\4x^2-24x+20=0$
Factor out $4$ to obtain:
$4(x^2-6x+5)=0$
Factor the trinomial to obtain:
$4(x-5)(x-1)=0$
Divide $4$ to both sides to obtain:
$(x-5)(x-1)=0$
Use the zero-factor property by equating each factor to zero.
$x-5=0$ or $x-1=0$
Solve each equation to obtain:
$x=5$ or $x=1$.
Upon checking, only $5$ satisfies the original equation.
Thus, the solution to the given equation is $\color{blue}{x=5}$.