\[\begin{array}{l}
x - \sqrt {2x - 5} = 4\\
dk:x \ge \frac{5}{2}\\
\Leftrightarrow \sqrt {2{\rm{x}} - 5} = x - 4\\
\Leftrightarrow \left\{ \begin{array}{l}
x - 4 \ge 0\\
2{\rm{x}} - 5 = {\left( {x - 4} \right)^2}
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x \ge 4\\
2{\rm{x}} - 5 = {x^2} - 8{\rm{x}} + 16
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\begin{array}{*{20}{l}}
{x \ge 4}
\end{array}\\
{x^2} - 10{\rm{x}} + 21 = 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\begin{array}{*{20}{l}}
{x \ge 4}
\end{array}\\
{x^2} - 7{\rm{x}} - 3{\rm{x}} + 21 = 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\begin{array}{*{20}{l}}
{x \ge 4}
\end{array}\\
x\left( {x - 7} \right) - 3\left( {x - 7} \right) = 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\begin{array}{*{20}{l}}
{x \ge 4}
\end{array}\\
\left( {x - 7} \right)\left( {x - 3} \right) = 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\begin{array}{*{20}{l}}
{x \ge 4}
\end{array}\\
\left[ \begin{array}{l}
x - 7 = 0\\
x - 3 = 0
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\begin{array}{*{20}{l}}
{x \ge 4}
\end{array}\\
\left[ \begin{array}{l}
x = 7\left( {tm} \right)\\
x = 3\left( {ktm} \right)
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow x = 7\left( {tm} \right)\\
vay:x = 7
\end{array}\]