NOT EXPLICITLY DISCLOSED WITHIN THE FILM, but less than 40 days.
The script of the film states it takes the Marines 3 weeks @FTL (Faster than light) to reach the planet, and the settlers signalled for help the day they were attacked.
The extended edition of the movie explains that even though distress signals travel beyond FTL, it would still take 2 weeks for the signal to arrive on earth.
2 weeks signal time (approx) + 3 weeks travel (approx) + mobilisation window (a few days) ≅ <40 days.
There are also hints all the settlers didn't die in the initial attack on the colony, such as half eaten food (Donuts!) that look fairly recent. It's unlikely a donut would have remained fresh for 5 weeks...