  Given a set of points $S \subseteq \mathbb{R}^2$, a subset $X \subseteq S$
with $|X|=k$ is called $k$-gon if all points of $X$ lie on the boundary of the
convex hull of $X$, and $k$-hole if, in addition, no point of $S \setminus X$
lies in the convex hull of $X$. We use computer assistance to show that every
set of 17 points in general position admits two disjoint 5-holes, that is,
holes with disjoint respective convex hulls. This answers a question of Hosono
and Urabe (2001). We also provide new bounds for three and more pairwise
disjoint holes.
  In a recent article, Hosono and Urabe (2018) present new results on
interior-disjoint holes -- a variant, which also has been investigated in the
last two decades. Using our program, we show that every set of 15 points
contains two interior-disjoint 5-holes.
  Moreover, our program can be used to verify that every set of 17 points
contains a 6-gon within significantly smaller computation time than the
original program by Szekeres and Peters (2006). Another independent
verification of this result was done by Mari\'c (2019).
