= Solution
Let $p(x)=x^3-5x-1$. Its values at useful points are
$$
p(-3)=-13,\quad p(-2)=1,\quad p(-1)=3,\quad p(0)=-1,\quad p(2)=-3,\quad p(3)=11.
$$
Since a <polynomial> is a <continuous function>, the <intermediate value theorem> gives one <polynomial root> in each of the disjoint intervals $(-3,-2)$, $(-1,0)$ and $(2,3)$. A nonzero <cubic polynomial> has at most three distinct <polynomial roots>. Hence it has
$$
\boxed{\text{exactly three distinct real roots}.}
$$
These three distinct <polynomial roots> already exhaust its <degree of a polynomial>, so each has <multiplicity of a root> one.
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