Answer
The provided statement is true.
Work Step by Step
It is known the nth term of an arithmetic sequence is;
\[{{a}_{n}}=a+\left( n-1 \right)d\]
Where a is first term, n is term, and d is common difference.
\[\begin{align}
& a=5 \\
& {{a}_{3}}=-3
\end{align}\]
So,
\[\begin{align}
& -3=5+\left( 3-1 \right)d \\
& 2d=-3-5 \\
& d=\frac{-8}{2} \\
& =-4
\end{align}\]
Now, the fourth term is;
\[\begin{align}
& {{a}_{4}}=5+\left( 4-1 \right)\left( -4 \right) \\
& =5+\left( 3 \right)\left( -4 \right) \\
& =5-12 \\
& =-7
\end{align}\]
Hence, the fourth term is\[-7\].
Hence, the provided statement is true.
