Let S be the set of all $(\lambda, \mu)$ for which the vectors $\lambda \hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}, \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\mu \hat{\mathrm{k}}$ and $3 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}$, where $\lambda-\mu=5$, are coplanar, then $\sum_{(\lambda, \mu) \in \mathrm{S}} 80\left(\lambda^2+\mu^2\right)$ is equal to-