Find each of the following product:

To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices. However, use of these laws are subject to their applicability in the given expressions.

In the present problem, to perform the multiplication, we can proceed as follows:

$5 x^{2} \times 4 x^{3}=(5 \times 4) \times\left(x^{2} \times x^{3}\right)$

$=20 x^{5} \quad\left(\because a^{m} \times a^{n}=a^{m+n}\right)$

Thus, the answer is $20 x^{5}$.