Regarding Man City, they still have a really good chance of qualifying for the CL for next season. I think they will do it, especially now that it’s confirmed that 5th place in the PL will qualify.
You are looking at Liverpool, Arsenal, Nottingham Forest and two others. Who will the other two be is the question, I think Chelsea and Man City.
Liverpool, Arsenal, Nottingham Forest, Manchester City and Chelsea will make the UEFA Champions League next season. There have been quite alot of supporting actions coming from these clubs. Manchester City will not relent despite the UEFA concluding about a 5th place in EPL to qualify for the UCL next season. We've know Manchester City to be a club that's determined to win games and wouldn't give up on their dreams so easily. Pep Guardiola is here to coupled his winning and also instructing emerged direction for clean path.
Forgive me if I'm wrong but as far as I know you have mentioned five teams in total where the top four teams from each league qualify for the Champions League. If the top four teams are discussed then the five teams you mentioned here but any of the four teams will have a good chance of qualifying for the Champions League next season. You can safely assume that Liverpool and Arsenal will qualify for the Champions League next season now who are the remaining two teams. Other teams will compete well for the remaining two positions, but there will be more chances for Nottm Forest and Manchester City, although I still have doubts about Manchester City's position, but since this club has an experienced manager, I believe he will be able to perform his duties well and make Manchester City qualify for the Champions League next season.