First, let's simplify the expression $5a^3$²:

$5a^3$² = 5² $a^3$²
= 25 a^$3\ast 2$ = 25a⁶

Now, let's multiply b² by 25a⁶:

b² * 25a⁶ = 25b²a⁶

So the final answer is 25b²a⁶.