Tottenham's performance has not been that good recently; they are no longer performing the same way as they were at the beginning of the season, and Chelsea have shown some consistency recently. I think Chelsea are fighting to end the season at the top 4 in the table, and with all indications, I think they can continue performing this way. I believe they will do it, though I can’t guarantee Chelsea a win against Tottenham because Tottenham are also not a team to underestimate, and they won't want Chelsea to take over, so let's wait and see what Chelsea will do at the end of the season, since they have been improving. Let's see if they are going to continue this way till the end of the season.
Chelsea have surprised us quite often this season by beating teams like Aston Villa, Man United, Newcastle and two weeks ago they beat Tottenham. Chelsea even held Man City to a draw. But sometimes this team also suddenly experiences bad luck again. But for now Chelsea looks better and more consistent. And if this continues then reaching rank 5 might be possible. But reaching rank 4 I don't think will be easy and I don't see the potential for that to happen. Luckily, Chelsea's remaining 3 matches this season are all easy matches. And against Brighton is probably the only one that looks like it will be quite difficult. Although Brighton this season is actually not that good.
As you said Chelsea performance in their last three matches they have been playing well or dominant, like when they played against Everton scoring five goals, no one really expected that much from them. For them reaching rank 5 is not probably possible because of Newcastle. The match against Brighton will not be that difficult because of Brighton current performance, assuming from their previous games, it is only the match against Nottingham forest that will be difficult because Nottingham is fighting for the relegation board in the table.
Anything can still happen and the remaining matches will all be exciting and tense matches. And in my opinion, Brighton is not an easy opponent for Newcastle because they have just beaten Aston Villa who are ranked 4th in the standings, but in the next match Newcastle will be the favorite because they are playing in front of their supporters.
And it is true that Chelsea's performance has improved recently, but unfortunately it is nearing the end of the season and they were able to occupy 6th place in the standings before being stuck in the middle of the standings. And I think Chelsea will win the game against Nottingham Forest and although Nottingham Forest is not an easy opponent as they will be fighting to get out of the relegation zone and if Chelsea maintains their form they will win.
Newcastle and Chelsea still have a chance of being in fifth place and that depends on the results of their remaining matches.