If the magnitude of the vectors, $\overline {a} , \overline{b} , \overline{c}$ are 3, 4, 5 respectively and $\overline{a}$ and $\overline{b} + \overline{c}, \overline{b}$ and $( \overline{c} + \overline{a} ), \overline{c}\: and\: ( \overline{a} + \overline{b} )$ are mutually perpendicular, then find the magnitude of $( \overline{a} + \overline{b} + \overline{c} )$

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