Evaluate the following determinant.
\[
\left|\begin{array}{ccc}
-1 & 5 & 5 \\
3 & -1 & 4 \\
-3 & 0 & 4
\end{array}\right|
\]

Step 1 ：Given the matrix: \[\begin{bmatrix} -1 & 5 & 5 \\ 3 & -1 & 4 \\ -3 & 0 & 4 \end{bmatrix}\]

Step 2 ：We can calculate the determinant of a 3x3 matrix using the formula: \[\text{det}(A) = a(ei−fh)−b(di−fg)+c(dh−eg)\]

Step 3 ：Where: \[a, b, c\] are the entries of the first row, \[d, e, f\] are the entries of the second row, and \[g, h, i\] are the entries of the third row.

Step 4 ：In this case, we have: \[a = -1, b = 5, c = 5, d = 3, e = -1, f = 4, g = -3, h = 0, i = 4\]

Step 5 ：Substituting these values into the formula, we get: \[\text{det}(A) = -1((-1)(4)−(4)(0))−5((3)(4)−(4)(-3))+5((3)(0)−(-1)(-3))\]

Step 6 ：Simplifying this expression, we find that the determinant of the given matrix is \(\boxed{-131}\)