Derek McInnes takes charge of Aberdeen for the first time on Monday night when they open their post-split campaign against Hibernian at Easter Road.
A 1-0 defeat by Dundee United in Craig Brown's final match in charge consigned Aberdeen to a fourth consecutive season in the bottom six and Reynolds admits they need to show their supporters there is scope for improvement.
Reynolds said: "It's five big games. I know the season is over in terms of doing something in the league but I think everyone is looking forward towards next season now.
"The fans and players want to build something and it's important we show a style of football and that the team he (McInnes) is going to put together can do something next season - and excite the fans and bring them in.
"There are five massive games. We are looking to win the five of them and have spoken about that. There is no reason why we can't. On our day we are as good as anyone in the league.
"It's important we show the supporters that we will have a decent team next year and that it's going to be something that can challenge at the right end of the league."
Aberdeen face a Hibs side on a high following their William Hill Scottish Cup semi-final comeback against Falkirk but Reynolds has noticed a fresh spark about the Dons squad since McInnes started taking training.
"When a new manager comes in there is a wee bit extra energy and brightness with new ideas," added Reynolds.
"Everyone is out to impress - players who have been playing want to show why they have been getting the nod and the other players are trying to show why they should be there."