Đáp án:
$\begin{array}{l}
a)\left| x \right| = 5 \Rightarrow \left[ \begin{array}{l}
x = 5\\
x = - 5
\end{array} \right.\\
b)\left| x \right| < 2 \Rightarrow - 2 < x < 2\\
4){\left( {2x + 1} \right)^2} = 25\\
\Rightarrow {\left( {2x + 1} \right)^2} = {5^2} = {\left( { - 5} \right)^2}\\
\Rightarrow \left[ \begin{array}{l}
2x + 1 = 5\\
2x + 1 = - 5
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
x = 2\\
x = - 3
\end{array} \right.\\
5){5^{x + 2}} = 625\\
\Rightarrow {5^{x + 2}} = {5^4}\\
\Rightarrow x + 2 = 4\\
\Rightarrow x = 2\\
19){x^2} + x = 0\\
\Rightarrow x\left( {x + 1} \right) = 0\\
\Rightarrow \left[ \begin{array}{l}
x = 0\\
x + 1 = 0
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
x = 0\\
x = - 1
\end{array} \right.
\end{array}$
