Divisible by 5?

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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