$\text{If}A\left(\text{adj}A\right)=\left[\begin{array}{ccc}-5& 0& 0\\ 0& -5& 0\\ 0& 0& -5\end{array}\right],\text{then the value of}\left|A\right|\text{is}$

The correct option is -5.

To understand why this is correct, we can recall the standard property of matrices relating a square matrix $A$ of order $n$ and its adjoint matrix $adj\left(A\right)$:
$$A\left(\text{adj}A\right)=\left|A\right|I_n$$
where $\left|A\right|$ represents the determinant of matrix $A$, and $I_n$ is the identity matrix of order $n$.

In this problem, we are given a 3 × 3 matrix:
$$A\left(\text{adj}A\right)=\left[\begin{array}{ccc}-5& 0& 0\\ 0& -5& 0\\ 0& 0& -5\end{array}\right]$$

We can factor out the scalar value $-5$ from this matrix:
$$A\left(\text{adj}A\right)=-5\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$$

Since $\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$ is the identity matrix $I$ of order 3, we can rewrite the equation as:
$$A\left(\text{adj}A\right)=-5I$$

By comparing this with the standard property $A\left(\text{adj}A\right)=\left|A\right|I$, we directly obtain:
$$\left|A\right|=-5$$