HMMT November 2023 U4

The number 5.6 may be expressed uniquely (ignoring order) as a product $\underline{a} \cdot \underline{b} \times \underline{c} . \underline{d}$ for digits $a, b, c, d$ all nonzero. Compute $\underline{a} \cdot \underline{b}+\underline{c} \cdot \underline{d}$.