Solve the equation
$$
\sqrt{x^{2}+5 x-2}-\sqrt{x^{2}+5 x-5}=1 . \text { (1) }
$$
Solve: Multiply both sides of (1) by the conjugate radical
$\sqrt{x^{2}+5 x-2}+\sqrt{x^{2}+5 x-5}$, we get
$$
\checkmark \sqrt{x^{2}+5 x-2}+\sqrt{x^{2}+5 x-5}=3 \text {. }
$$
$$
\text { By } \frac{(1)+(2)}{2} \text { we get } \sqrt{x^{2}+5 x-2}=2 \text {, }
$$

i.e., $x^{2}+5 x-6=0$.
Solving it, we get $x_{1}=1, x_{2}=-6$.
Upon verification, $\mathbf{x}_{1}=1$ and $x_{2}=-6$ are indeed the roots of the original equation.