I have looked at buying a particular 2004 nissan altima. It seems to be in pretty good shape; good price with only 75k miles on it. It's a 5 speed and when I changed from 1st to 2nd and between 2nd to 3rd, the engine revved up. It didn't do this between 3rd and 4th and 4th and 5th. I've driven several 5 speed cars before and I've never noticed the engine revving up when changing the gears. What could this be? The car comes with a 1yr/15000 mile warranty. I'm not sure if I want to purchase the car if something is wrong with it.

I live about 2 hrs away from the vehicle and with my work schedule, it's very difficult for me to just take the car to a mechanic to get it checked out. I've already taken one day off from work to go look at the car and I didn't purchase it because of this issue. The dealer said there is nothing wrong with it.

Any clues?

Thanks in advance and Merry Christmas!

Any clues? - Yes. What you are describing sound like the clutch disc is worn. Unless you are inadvertently slipping the clutch with your foot, the clutch will need serviced soon.
If the dealer you're buying the car from is confident there is no problem, ask for a written warranty. Make certain that you stipulate the clutch and related components in that warranty so the dealer cannot claim later that it's a "wear" item.