The magnitude of a vector \(\mathbf{v} = a\mathbf{i} + b\mathbf{j}\) is given by \(\|\mathbf{v}\| = \sqrt{a^2 + b^2}\). For \(\mathbf{v} = 3\mathbf{i} - 5\mathbf{j}\), we have \(a = 3\) and \(b = -5\). Thus,
\[
\|\mathbf{v}\| = \sqrt{3^2 + (-5)^2} = \sqrt{9 + 25}
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