I'm always an optimist, so...
West Ham (H) - Win
Everton (A) - Win
Spurs (H) - Win
Southampton (A) - Win
Man City (H) - Draw
13 points.
We showed last season we could go on an incredible run, and it's been well documented how we are set-up to be stronger in the 2nd half of the season. We have Sturridge coming back at some point during these 5 games, and we have arguably a better squad than last year, with players like Can, Markovic, Moreno, and Lallana in really good form and getting better each week. Coutinho, Lucas and Sakho are also consistently putting in great performances.
The big factor will be the cups - this time last year we were out of the league cup, had no European games, and we went out of the FA cup in mid-February. If we go on more cup runs and get deep into the Europa and FA competitions, then our squad will be strongly tested.