Yes, you have 5 points towards the challenge but this equals to 4 points towards each faction's contract.
First quest gives 1 point to one faction (just one). Second quest gives 1 point to the other faction (again, just one). Third, fourth and fifth quests give 1 point to each faction (to both).
So one faction will have 4 points (from 1st, 3rd, 4th and 5th quests) and the other faction will have also 4 points (from 2nd, 3rd, 4th and 5th quests).