Directed Graphs and Network Flows · Hard problem

A $5$-team tournament has results $1\to2$, $2\to3$, $3\to1$, $1\to4$, $4\to2$, $3\to4$, $1\to5$, $5\to2$, $5\to3$, $4\to5$. What is the smallest number of individual games whose winner and loser would need to be swapped so that the results become transitive (admit a ranking of the $5$ teams with every game won by the higher-ranked team)?