$x^{5} \cdot x^{3}$

Step 1 ：Understand the problem: We are asked to simplify the expression $x^{5} \cdot x^{3}$.

Step 2 ：Recall the rule of exponents: $a^{m} \cdot a^{n} = a^{m+n}$.

Step 3 ：Apply the rule to the given expression: $x^{5} \cdot x^{3} = x^{5+3}$.

Step 4 ：Perform the addition in the exponent: $x^{5+3} = x^{8}$.

Step 5 ：Check the result: $x^{8}$ is indeed the simplest form of the expression $x^{5} \cdot x^{3}$.

Step 6 ：So, the final answer is \(\boxed{x^{8}}\)