Maybe Chelsea doesn't have a big enough chance to take 5th place from Tottenham because the Premier League doesn't have many matches left. Apart from that, even though Tottenham Hotspur is in poor performance, Newcastle could be an obstacle because they have also been playing quite well recently.
Tottenham is quite safely at their fifth position and Chelsea now looks similar to Liverpool last season. Rising performances of Liverpool in latest weeks of last season were not enough for them to get a fourth position from Newcastle United. This season Chelsea are facing with a same disappointed fact but they firstly must feel happy with their recent performances. They are improving a lot recently and are harvesting their training, efforts with good results lately.
But what is certain is what Chelsea have gone through and achieved now, I think it could be very important capital for their preparations for next season. So all they need to do is keep it all going and maybe make a little improvement and sign new players whose existence is truly necessary.
Chelsea can use this season, even very last matches, to improve connections of their players and prepare for a next season. With more trainings in the summer and maybe some new players to enhance their squad quality, Chelsea will return to Premier League next season as a very competitive team and will fight strongly for top four position.