Bipartite Graphs and Matchings · Hard problem

People $P,Q,R$ are each qualified only for opening $1$; person $S$ is qualified for openings $\{2,3\}$; person $T$ is qualified for $\{4,5\}$ (five people, five openings $1$–$5$). What is the minimum number of new qualifications (edges) that must be added so that all five people can be placed in distinct openings?