On Turán numbers for disconnected hypergraphs

We introduce the following simpler variant of Tur\'an problem: Given integers $n>k>r\geq 2$ and $m\geq 1$, what is smallest integer $t$ for which there exists an $r$-uniform hypergraph with $n$ vertices, edges $m$ connected components such that any $k$-subset vertex set contains at least one edge? prove some general estimates this quantity its limit, normalized by $\binom{n}{r}$, as $n\rightarrow \infty$. Moreover, we give a complete solution problem particular case when $k=5$, $r=3$ 2$.