As Tyler said, 5' works with a bivy. I would add that it works as long as you are on relatively level ground and don't slide out from under. The narrow tarp also works very well for hammocks and I've lived under one for half a year at a time. However, for ground pitching, I really prefer something wider.
Obviously, you want a longer tarp. If you stick with a flat rectangle, the weight will compound quickly as you widen, say, a 10 or 11 foot tarp. You might consider a hexagonal tarp that forms its own beaks on the ridgeline. Beaks improve coverage while minimizing weight. Beaks can be flat and you can add tabs that fold them into downward-angled hoods which shed wind better and give better protection from blown rain.
I'm a taller guy, and feel comfortable with an irregular hexagon, 11.5' along the ridge (beak end to beak end)and 7.5' across the middle. The sides are 6'. I put mosquito net around the edges to form a curtain (we have West Nile Virus here) and use a separate groundsheet.