First Time Home Owners Question?

we have our home up for sale and have had quiet a few lookers. we spoke with someone who is very interested in the home and wants to get the ball rolling. they asked us to $5,000 off the asking price because they said they wanted the carpet replaced. the carpet is not brand new but in good condition. we steam clean it about twice a month. none of the other lookers had any complaints about it either. were thinking that they’re only saying this because its the only excuse they could come up with for financial negotiations. we want to sell the home asap but don’t want to settle for anything less then the asking price. we had a realtor look at it and she said that were selling it at a fair deal. no one else has made any offers on the house and this worries us also. does anyone have any solutions to this problem? any advice is appreciated!