8 points from the last 5 games= 1.6 points per game.
13 remaining games x 1.6 points = 20.8 points. (Say 21).
Total 37 points, probably enough to overtake Sunderland and Norwich.
If Newcastle take 13 points from their 13 games (a point per game which is slightly better than they have achieved so far) they finish on 37 points as well.
Our goal difference is presently -20, theirs is -18. That changes with our better results than them.
Conclusion:We are staying up as Newcastle are relegated on goal difference.
Simples.