If `vec(a)` and `vec(b)` are perpendicular vectors such that `|vec(a)+vec(b)|=13 and |vec(a)|=5`,

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If `vec(a)` and `vec(b)` are perpendicular vectors such that `|vec(a)+vec(b)|=13 and |vec(a)|=5`, find the value of `|vec(b)|`.
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