Possibly it can be 6 spots giving to England. Currently 5 is inevitable what they should be hoping for that is that Arsenal or Aston Villa make a way for them while Chelsea wins the FA Cup and Manchester United win Lyon in the quarter final stage of the Europa league competition then surely it makes up like six to go the next season UCL competition.
We will see how everything will turn out to be in the end. If it is six then it is better because Manchester City and Chelsea will surely have a chance. But if it is just 5 probably one has to go.
Even right now England have good chance of have 6 spots for next season, but you're all calculation is wrong because Chelsea is already out of the FA Cup, so this is not going to work for them to have spot in next season Champions League. Currently, Liverpool, Arsenal and Nottingham Forest are strong for going into Champions League with 2 spots available three teams fighting hard Chelsea, Manchester City and Newcastle United after this Manchester United and Tottenham both are in Europa Cup with strong case for have won this can give them 6th spot in Champions League.
After this all-last option is if Premier League clubs have more spots are Aston Villa won Champions League because this will give them 7th spot, but this is surely not easy as they are going to face PSG and then have Arsenal/ Real Madrid challenge which is also not easy.