We know a relation $R$ defined on $\{1,2,3,4,5\}$ is transitive. We also know that $(1,2),(2,3),(3,4),(4,5)$ are all in $R.$ Which of the following tuples are for sure also in $R?$

$(1,3)$

$(1,5)$

$(4,5)$

$(2,5)$

$(5,2)$