To find the algebraic expression that represents "the price of the shoes decreased by 5 dollars," we need to carefully interpret the phrase.
1. Identify the original price: The variable [tex]\( p \)[/tex] represents the original price of the pair of basketball shoes.
2. Understand the change: The phrase "decreased by 5 dollars" indicates a reduction in the price by 5 dollars.
To represent this mathematically, we subtract 5 from the original price [tex]\( p \)[/tex].
So, the expression for the new price after the decrease would be [tex]\( p - 5 \)[/tex].
Let's examine the choices given:
- A. [tex]\(\frac{p}{5}\)[/tex]: This represents the price divided by 5, which does not match the problem statement.
- B. [tex]\(p - 5\)[/tex]: This correctly represents the price decreased by 5 dollars.
- C. [tex]\(5p\)[/tex]: This represents the price multiplied by 5, which does not match the problem statement.
- D. [tex]\(p + 5\)[/tex]: This represents the price increased by 5 dollars, which is the opposite of what is described.
Hence, the correct algebraic expression is [tex]\( \boxed{p - 5} \)[/tex].
