Postulation of general quintuple fat point schemes in P3P3

We study the postulation of a general union Y   of double, triple, quartuple and quintuple points of P3P3. In characteristic 0, we prove that Y   has good postulation in degree d⩾11d⩾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.