4 wins gives us 69 points.
For our rivals to get to 69 points:
Newcastle need 2 wins and a draw against Brighton (a), Chelsea (h), Arsenal (a), Everton (h)
Man City need 2 wins and 2 draws against Wolves (h), Southampton (a), Bournemouth (h), Fulham (a)
Chelsea need 3 wins against Liverpool (h), Newcastle (a), Man Utd (h), Forest (a)
Forest need 3 wins against Brentford (h), Palace (a), Leicester (h), West Ham (a), Chelsea (h)
I think we can assume Man City are going to do it, so that leaves 4 teams battling for 2 CL spots.
Forest have 3 winnable games - possibly 4, so their final game against Chelsea may be irrelevant. We need them to have a drop off.
Newcastle have tricky games, but they're good at home. So they'd need to pick up a point against Brighton or Arsenal (who will be resting for the CL if they get to the Final or will be on the beach if they don't).
I think Chelsea have the toughest run, and games against Newcastle and Forest. I don't think they'll make Top 5.
So I think we need to win all 4 games, and hope for Newcastle to slip up; as I think Man City and Forest will get 2 of the 3 remaining spots.