For the average person, a $5000 bike isn't much better than a $1000 one at least. The biggest bump you get is going from a big box store bike to a bike shop bike. In this case, brand doesn't really matter. A Globe or Townie at a bike shop is better than something at a Walmart, a bike shop Schwinn is not the same as a big box Schwinn.

At the bike shop, as you go up in price you start getting upgraded components, carbon fork until you get all the way up to a full carbon bike with top end components. Is a full carbon bike the best you can get? Not necessarily. You wouldn't want one for touring for example, you want something that can handle weight. Good ol steel being the best.

The bike is important but at the top end, it's diminishing returns for the average person. For me, I don't see myself spending more than $1500 for a bike, but the $500 bikes don't work for me anymore either.