Vectors $\mathbf{a}$ and $\mathbf{b}$ satisfy $\|\mathbf{a}\| = 5$ and $\|\mathbf{b}\| = 4.$  Also, the angle between vectors $\mathbf{a}$ and $\mathbf{b}$ is $60^\circ.$  Find $\|\mathbf{a} - \mathbf{b}\|.$
<|im_start|>system
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<|im_start|>user
Vectors $\mathbf{a}$ and $\mathbf{b}$ satisfy $\|\mathbf{a}\| = 5$ and $\|\mathbf{b}\| = 4.$  Also, the angle between vectors $\mathbf{a}$ and $\mathbf{b}$ is $60^\circ.$  Find $\|\mathbf{a} - \mathbf{b}\|.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
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Vectors $\mathbf{a}$ and $\mathbf{b}$ satisfy $\|\mathbf{a}\| = 5$ and $\|\mathbf{b}\| = 4.$  Also, the angle between vectors $\mathbf{a}$ and $\mathbf{b}$ is $60^\circ.$  Find $\|\mathbf{a} - \mathbf{b}\|.$
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