Let $Y$ be an 5 dimensional closed subscheme of $P^{n} — Y$ and $p (P^{n} — Y)$ the largest integer $p$ such that $H^{i} (P^{n} — Y,L)$ is finite dimensional for all $i < p$ and for all locally free sheaves $L$ on $P^{n} — Y$. If we introduce the same integer $p (P^{n} — Y^{a})$ in the complex case, i.e. when $L$ runs through the set of all locally free analytic sheaves on $P^{n} — Y^{a}$, we show that $p (P^{n} — Y^{a}) = n—s—1$ if $p (P^{n} — Y)= n—s—1$.