Jason Roy and Craig Overton miss out with Ben Stokes set to play as a specialist batsman.
Woakes, who played the first three matches of the series before missing the defeat at Old Trafford, comes back in with Curran given the nod in place of Overton.
Roy's struggles at the top and in the middle of the order see him dropped with Stokes set to move up. The ECB say he has a shoulder injury which means he won't bowl.
Captain Joe Root said that Roy had missed out due to Stokes' injury, which meant the side needed re-balancing.
"It's always tough to leave guys out, but Stokesy obviously picked up a shoulder injury in the last game and won't be able to bowl the overs we normally expect him to," Root said at a press conference.
"With that we've had to change the balance of the side, and Jason's the unfortunate one to miss out.
"Jason's had an opportunity to come in and play Test cricket, get a feel for it and it's not quite gone how he would have liked.
"But I'm sure he'll go away and work extremely hard and come back again.
"That's what you expect of guys when they get left out and I'm sure he'll have that attitude and will want to try and prove a point and get himself back into the side."
England team for fifth Ashes Test:
Joe Root (c), Jofra Archer, Jonny Bairstow (wk), Stuart Broad, Rory Burns, Jos Buttler, Sam Curran, Joe Denly, Jack Leach, Ben Stokes, Chris Woakes.