There is a math teacher in a school whose favorite number is a positive integer (let's call it $x).$ She told her 5 students--Alice, Beatrice, Candice, Denise, Eunice--the number $x,$ and the following conversation took place:

**Alice:** "$x+1$ is not divisible by 5."

**Beatrice:** "$x+2$ is not divisible by 5."

**Candice:** "$x+3$ is not divisible by 5."

**Denise:** "$x+4$ is not divisible by 5."

**Eunice:** "$x+5$ is not divisible by 5."

Without knowing $x$, can we guarantee that at least one of these 5 students is lying?

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