England not dependent on Anderson - Cook
Anderson delivered a 13-over spell on the final morning to break the back of the Australian resistance and then, despite an attack of cramp, was forced back into service to claim the final wicket. He finished with 10 for 158 in the match and bowled a total of 55.5 overs earning England a 14-run victory and himself the Man-of-the-Match award.
Cook did admit, however, that Anderson had carried a heavy burden in this game and accepted that workload concerns were an issue with the second Investec Ashes Test beginning at Lord's on Thursday and nine more Ashes Tests to come before the end of January.
"Jimmy was outstanding," Cook said afterwards. "He always wants one more over, though 13 was probably quite a lot in that first hour.
"But no, I don't think we're over-reliant on him at all. He's a world-class bowler and you sometimes use him in these situations when you know there's a time-frame. He had an amazing rhythm in this game.
"Stuart Broad and Steven Finn have done outstandingly well for us over a huge amount of time, but it just happened to be Jimmy's day and Jimmy's game. Sometimes it happens like that.
Yeeeaaahhhhh!!! Emotional rollercoaster what a great Test match win! Atmosphere was insane I love Trent Bridge!!— Stuart Broad (@StuartBroad8) July 14, 2013
"When a bowler hits a rhythm you just keep asking him if he's feeling alright. That's why you do the training in the gym: when your captain needs you to do it you are physically fit to do it. We know his skill but his heart to keep running in on a hot day on a flat wicket was outstanding.
"No, there's no bowler in the world I'd rather have. Not in any conditions. These were very subcontinent conditions and he was outstanding. He swings it both ways on an immaculate length and makes it very hard to score.
"You do worry about his workload in one sense but, when you're out in the middle, that is kind of irrelevant. You have to think about what is best for the team at that precise time. You can't be thinking about what will happen in two months time.
"It's the job for our backroom staff and us as a team to make sure we recover well because back-to-back Test matches are hard physically. We have to come back for Thursday ready."
Cook scored Test runs galore in Australia two years ago but his first Ashes Test as captain was something different. "I always said I would be the only England captain not to go bald, but after days like today, it might not help that," he said.
What an amazing atmosphere and test match! Amazing! #ashes— Joe Root (@joeroot05) July 14, 2013
Asked by Sky Sports whether it had been his best performance in an England shirt, Anderson said: "Yeah I'd say so. We knew it wasn't going to be easy at the start of the day, but I thought the lads stuck to it and stayed calm when it was getting tough.
"I'm just delighted to get the win. I had the nerves going a little bit but I love bowling here, it's been good to me over the years and I'm happy that I could pick up some more wickets.''
Asked if he could maintain the same levels of workload across the series, he said: "If I'm bowling 13-over spells it's going to be difficult! But it's Ashes cricket. I love playing Test match cricket and the Ashes is right up there, and that's why we do the hard work in the gym - to get out there and bowl long spells.''
Australia's captain, Michael Clarke, was proud of his team in defeat but credited England's victory to the efforts of Anderson and Ian Bell, who made the only century of the match.
"I think the boys can certainly hold their head high. It was a wonderful game of cricket. Credit to England. England fought hard really hard throughout the five days and I think the two best performers of the Test match were Ian Bell making a hundred and Jimmy Anderson getting five-for in each innings, so they deserved the win."
George Dobell is a senior correspondent at ESPNcricinfo