In Chapter V of The Great Gatsby what arouses Nick's suspicions about Gatsby's past? What suspicion does this apparent lie reinforce?
By the time the reader reaches Chapter V in Gatsby, he or she realizes that Nick doubts the veracity of many of Gatsby's statements. For example, the whole time that Gatsby tells Nick about his background, he keeps looking over to the side at Nick to see if he is "buying" his story. Gatsby also just happens to have his war medal and photo of his time at Oxford with him to provide proof to Nick that he is telling the truth.
Thus, in Chapter 5 when Gatsby tells Nick that it took him "just three years to earn the money that bought" his immense house, Nick is ready to challenge Gatsby. He says to Gatsby:
I thought you inherited your money.
Gatsby is quick on his feet and tells Nick that he lost most of his money in the "panic" and then almost makes Nick feel guilty for questioning him. He must convince Nick that he was not lying about inheriting his money for two reasons. First, he wants Nick to believe and trust him. Secondly, Gatsby wants so badly to fit in with the "Old Money" crowd, and he will not be able to do so if people know that he earned his money, especially through illegal means.
In answer to your second question, the lie reinforces Nick's general disbelief in Gatsby's history. It is not that he dislikes Gatsby--he actually wants to believe the millionaire, but as an objective narrator, Nick simply cannot overlook Gatsby's lies because he likes him.