# Why is a smooth algebraic surface in $\mathbb{P}_{\mathbb{C}}^3$ of degree 5 simply connected?

The title says it all.

In fact, i am only trying to prove that if $S$ is an irreducible smooth algebraic surface of degree 5 in $\mathbb{P}_{\mathbb{C}}^3$ (hence a four dimensional manifold over the reals), its first singular cohomology group $H_1(S ; \mathbb{Z})$ contains no two torsion.

I know only that by the short exact sequence of the sheaf of ideals and hodge theory that this group has no free part. But for the torsion part i have no idea.

Any help would be really appreciated, i would prefer hints over a complete answer!

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