The magnitude of a vector is calculated as the square root of the sum of the squares of its components. For the vector $-5\mathbf{i}+3\mathbf{j}-\mathbf{k}$, the magnitude is calculated as follows:
\[||\mathbf{A}|| = \sqrt{(-5)^2 + 3^2 + (-1)^2} = \sqrt{35}\]
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