Find each of the following product:

To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, $a^{m} \times a^{n}=a^{m+n}$, wherever applicable.

We have:

$(-5 x y) \times\left(-3 x^{2} y z\right)$

$=\{(-5) \times(-3)\} \times\left(x \times x^{2}\right) \times(y \times y) \times z$

$=15 \times\left(x^{1+2}\right) \times\left(y^{1+1}\right) \times z$

$=15 x^{3} y^{2} z$

Thus, the answer is $15 x^{3} y^{2} z$.