  We prove that strength and slice rank of homogeneous polynomials of degree $d
\geq 5$ over an algebraically closed field of characteristic zero coincide
generically. To show this, we establish a conjecture of Catalisano, Geramita,
Gimigliano, Harbourne, Migliore, Nagel and Shin concerning dimensions of secant
varieties of the varieties of reducible homogeneous polynomials. These
statements were already known in degrees $2\leq d\leq 7$ and $d=9$.
