$\begin{align}  & {{a}_{5}}+{{a}_{13}}=2{{a}_{9}} \\  & {{a}_{7}}+{{a}_{11}}=2{{a}_{9}} \\  & {{a}_{9}}+2{{a}_{9}}+2{{a}_{9}}=125\Rightarrow 5{{a}_{9}}=125\Rightarrow {{a}_{9}}=25={{a}_{1}}+8d \\  & {{S}_{17}}=\frac{17}{2}\left[ 2{{a}_{1}}+16d \right]=17\left[ {{a}_{1}}+8d \right]=17\times 25=425 \\ \end{align}$