Five-vertex model and lozenge tilings of a hexagon with a dent

We consider the five-vertex model on a regular square lattice of the size $L \times M$ with boundary conditions fixed in such a way that configurations of the model are in one-to-one correspondence with the lozenge tilings of the hexagon with a dent. We obtain two determinant representations for the partition function. In the free-fermionic limit, this result implies some summation formulae for Schur functions.