If A is a square matrix of order 5, then $\left|5A\right|$ is equal to

When a matrix is multiplied by a constant, every element is multiplied with the constant. 

In case of determinant the common factor in any row can be taken out from that row. 

$\therefore \left|5\mathrm{A}\right|=5^5\left|\mathrm{A}\right|$