We couldn't have got 9 this season. 8 was max as things had gone. But in theory...
If CL & EL were won by teams outside of Europe qualification we'd get 5 CL spots as you said.
However the 4th place in league wouldn't take an existing EL spot. It's actually an extra EL spot.
"3.09 If the UEFA Champions League titleholder and the UEFA Europa League
titleholder come from the same association and do not qualify for the
competition through their domestic championship, one of the following scenarios
applies:
...
c. If the association is entitled to four places in the UEFA Champions League and
neither titleholder qualifies for the UEFA Europa League through its domestic
championship, the lowest-placed of the association’s UEFA Champions League
representatives is automatically transferred to the UEFA Europa League (into
the UEFA Europa League group stage and the access list will be rebalanced
accordingly). In this case, the association of the titleholders is entitled to one
additional place (total of five) in the UEFA Champions League and one
additional place (total of four) in the UEFA Europa League."