To translate the given situation into an inequality, let's break down the statement step by step.
Step 1: Understand the problem statement.
We are given that "[tex]\(\frac{3}{5}\)[/tex]" times "5 less than a number" is "no more than 27".
Step 2: Define the variable.
Let [tex]\(x\)[/tex] represent the number.
Step 3: Express "5 less than a number" algebraically.
"5 less than a number [tex]\(x\)[/tex]" can be written as [tex]\(x - 5\)[/tex].
Step 4: Set up the multiplication.
We are told that [tex]\(\frac{3}{5}\)[/tex] times [tex]\(x - 5\)[/tex], which can be written as:
[tex]\[
\frac{3}{5}(x - 5)
\][/tex]
Step 5: Translate "is no more than 27" into an inequality.
The phrase "is no more than 27" means that the expression should be less than or equal to 27. Thus, we write:
[tex]\[
\frac{3}{5}(x - 5) \leq 27
\][/tex]
Step 6: Compare with the given options.
Among the provided options, the inequality:
[tex]\[
\frac{3}{5}(x - 5) \leq 27
\][/tex]
matches exactly with our translation.
Therefore, the correct inequality representing the given situation is:
[tex]\[
\boxed{\frac{3}{5}(x - 5) \leq 27}
\][/tex]
Consequently, the correct choice number corresponding to this inequality is [tex]\( \boxed{4} \)[/tex].
