$-x^2+4x > -5$

$x^2-4x - 5 < 0$

$(x-5)(x+1) < 0$

same thing as the last problem we check signs from $-\infty \to \infty$

$(-\infty, -1) \rightarrow +$

$(-1, 5) \rightarrow -$

$(5, \infty) \rightarrow +$

and so the solution is

$(-1,5)$

and thus you are correct and the book is not!