Postulation of general quintuple fat point schemes in P³

We study the postulation of a general union Y of double, triple, quartuple and quintuple points of P^3. In characteristic 0, we prove that Y has good postulation in degree $d\ge 11$. The proof is based on the combination of the Horace differential lemma with a computer-assisted proof. We also classify the exceptions in degree 9 and 10.