Why is ICl5 unstable?
The textbook answer must be wrong, since $\ce{IF5}$ is a sufficiently stable compound and fluorine is more electronegative than chlorine.

Rather, I think that the reason for $\ce{ICl5}$’s lesser stability is the lower electronegativity of chlorine. Creating this type of hypercoordinate compounds requires two sets of four-electron three-centre bonds of the $\ce{X- \bond{...}{I+}-X &lt;-&gt; X-{I+}\bond{...}X-}$ type. This type of bond requires a sufficient electronegativity on the outer atoms to stabilise the partial negative charge better — something fluorine is more capable of than chlorine. $\ce{ICl5}$ should only be possible because of iodine’s low electronegativity and $\ce{BrCl5}$ should be orders of magnitude less stable again.

A second aspect could be the larger size of chlorine atoms compared to fluorine atoms causing greater steric stress, longer bonds and therefore weaker interactions.