To determine which expression is equivalent to [tex]\((fg)(5)\)[/tex], we need to understand the notation involved.
1. Understanding [tex]\((fg)(x)\)[/tex]:
- When we see [tex]\((fg)(x)\)[/tex], this notation represents the composition of two functions [tex]\(f\)[/tex] and [tex]\(g\)[/tex] evaluated at [tex]\(x\)[/tex], specifically the product of the values of [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex].
- In mathematical terms, [tex]\((fg)(x) = f(x) \cdot g(x)\)[/tex].
2. Applying to [tex]\(x = 5\)[/tex]:
- We substitute [tex]\(x\)[/tex] with [tex]\(5\)[/tex] in the expression [tex]\((fg)(x)\)[/tex].
- Therefore, [tex]\((fg)(5)\)[/tex] is equivalent to [tex]\( f(5) \cdot g(5) \)[/tex].
3. Checking the given options:
- [tex]\( f(5) \times g(5) \)[/tex] directly corresponds to the product of [tex]\(f(5)\)[/tex] and [tex]\(g(5)\)[/tex].
- [tex]\( f(5) + g(5) \)[/tex] represents the sum of [tex]\(f(5)\)[/tex] and [tex]\(g(5)\)[/tex], which is not the same as their product.
- [tex]\( 5 f(5) \)[/tex] and [tex]\(5 g(5)\)[/tex] represent scaling [tex]\(f(5)\)[/tex] and [tex]\(g(5)\)[/tex] by 5, respectively, which does not match our requirement of their product.
By the process of elimination and direct interpretation, the correct equivalent expression for [tex]\((fg)(5)\)[/tex] is:
[tex]\[
\boxed{f(5) \times g(5)}
\][/tex]
Thus, the expression equivalent to [tex]\((fg)(5)\)[/tex] is the first option:
[tex]\[
\boxed{1}
\][/tex]
