To simplify the expression $(a^3)(a + 5)$, you can distribute $a^3$ across the terms inside the parentheses:

$(a^3)(a + 5) = a^3 \cdot a + a^3 \cdot 5$

Now, simplify each term:

$a^3 \cdot a = a^{3+1} = a^4$ $a^3 \cdot 5 = 5a^3$

So, the expression simplifies to:

$a^4 + 5a^3$

Would you like more details or have any other questions?

Here are five related questions you might find interesting:

1. How would you simplify $(a^2)(a^3 + a)$?
2. What is the result of multiplying $(x^3)(x - 7)$?
3. How do you factor $a^4 + 5a^3$?
4. Can you simplify $(2a^3)(3a^2 + 4a)$?
5. What is the degree of the polynomial $a^4 + 5a^3$?

Tip: Always combine like terms and use exponent rules when multiplying variables.