NetworkFlow[
 FromAdjacencyMatrix[{{Infinity, 5, 3, Infinity, Infinity,
    Infinity}, {0, Infinity, 2, 3, Infinity, Infinity}, {0, 2,
    Infinity, Infinity, 4, Infinity}, {Infinity, 0, Infinity,
    Infinity, 1, 2}, {Infinity, Infinity, 0, 0, Infinity,
    5}, {Infinity, Infinity, Infinity, 0, 0, Infinity}},
  EdgeWeight], 1, 6, Cut]