Well, it's been quite a night for Celtic. Barring a collapse, they will be in the group stage draw for the Champions League. Thanks for logging on to our coverage of the first leg in Glasgow. You'll find plenty more reaction on our website this evening and tomorrow. All the best.
More from Brendan Rodgers: "We want to go there and win the game. We're in a better place. We have to complete the second leg and finish the job off. There was lots of speculation about Nir Bitton. There's no-one knows better than me if he was good enough. I wouldn't play him if I didn’t think he was. He made a lot less mistakes than many centre-halves I see, that are actual centre-halves. I thought he was outstanding tonight - defending, taking the ball, he gives us the composure to build the game and when he is under pressure he has the ability to find a midfield player."
Celtic manager Brendan Rodgers: "Every game in this qualification is a pressure game. The pleasing aspect is how the players coped with that - their calmness in possession, how we circulated the ball and how we opened up the spaces and tired Astana out. They normally don’t press. Once we found our angles we could play through them that wee bit better. Some of our play was outstanding. It was very complete. We now need to get the job done in the second game."
Celtic manager Brendan Rodgers: "It's a great demonstration of the work that the players have made over the past season - the maturity, the belief in a shape and their understanding of the game. We scored five goals and we missed one or two chances. To do this against a team that a couple of years ago was drawing with Atletico Madrid and Benfica, I'm very proud of the team."
We're still waiting to hear what Brendan Rodgers has to say about his team's dismantling of Astana. The media conference is about to begin in the next few minutes.
Leigh Griffiths looks on as his shot is deflected off Igor Shitov into the Astana net for Celtic's fifth.Copyright: SNS
Celtic captain Scott Brown and some of his team-mates enjoy the post-match celebrations.Copyright: SNS
Former Celtic striker on BBC Sportsound
"It was a real mature performance. How much he has come on in the last year, it's been phenomenal to see. He is now the number nine for Scotland and that's because of the changes he has made in his game. Gordon Strachan now trusts him up there."
If you have time to stay with us we'll bring you some quotes from Celtic manager Brendan Rodgers.
Here are tonight's other results in the play-off first legs:
Hapoel Beer Sheva 2-1 Maribor
Istanbul Basaksehir1-2 Sevilla
Napoli 2-0 Nice
Olympiakos 2-1 Rijeka
James Forrest scores Celtic's fourth on their way to a 5-0 win, which Uefa says is a joint record-winning margin and a record home win in the Champions League play-offs.Copyright: SNS
Former Celtic players Scott McDonald and Pat Bonner, speaking on BBC Radio Scotland, are certain that Brendan Rodgers should take his full squad to Kazakhstan for Tuesday's return leg. No slacking.
Former Celtic goalkeeper on BBC Sportsound
"This shows you how far this team have come. Last year they were nervous but they got through to the group stage. European football is the benchmark to measure any Celtic team. I think they are a team that can now compete in the group stage. I think you have to talk them up now. They have Dembele and Boyata to come back in and they may add others. Brendan will be very ambitious. I think they can go into a group and get better results than last year."
Brendan Rodgers and his Celtic players take a stroll around the pitch applauding the fans, who return the compliment.
News coming to us that Uefa has "awarded" the fifth goal to Igor Shitov rather than Leigh Griffiths.
Celtic take a short corner in the dying seconds. When the whistle blows, Leigh Griffiths hoofs the ball into the stand and the celebrations begin.
What's encouraging for Celtic is that they have won this match, and surely the tie, without two near certain starters - defender Dedryck Boyata and striker Moussa Dembele, both of whom are out injured.
There are five minutes of injury time.
Astana are in disarray as Leigh Griffiths, in yet another move down the inside-right channel, knocks in Celtic's fifth goal, via a deflection. The Celtic fans are loving this. Griffiths is too.
"Celtic have gone through Astana like a blowtorch through butter tonight," Liam McLeod tells BBC Radio Scotland listeners.