Codegree-Constrained Turán Problems for $F_5$ and Its Blow-ups

Let $F_5$ denote the $3$-uniform hypergraph with edge set $\{abc,abd,cde\}$. For a hypergraph property $\mathcal P$, let $ex_{\mathcal P}(n,F_5)$ be the maximum number of edges in an $n$-vertex $F_5$-free $3$-uniform hypergraph satisfying $\mathcal P$. Let $Δ_2(H)$ denote the maximum codegree of a p