Question

Dy/dx=6+sqrt{y-6x+5}

Answer 1

In the future, please state exactly what you want to solve instead of only the problem itself.

Assuming you want to find the derivative and assuming I can treat the problem like it's a partial derivative (aka I can treat y as a constant) :
let u = y - 6x + 5
du = -6
dy/dx = 6 - (1/6)(u)^1/2 du
Integrate both sides
y = 6x -(1/9)(u)^(3/2)
y = 6x -(1/9)(y - 6x + 5)^3/2

Answer 2

Looks more like a differential equation to me:
\[\frac{dy}{dx}=6-\sqrt{y-6x+5}\]
Let's try a substitution, \(v=y-6x\), so that \(\dfrac{dv}{dx}=\dfrac{dy}{dx}-6\):
\[\begin{align*}
\frac{dv}{dx}+6&=6-\sqrt{v+5}\\
\frac{dv}{dx}&=-\sqrt{v+5}\\
\frac{dv}{\sqrt{v+5}}&=-dx
\end{align*}\]