Five miles is achievable in good conditions in a small boat using a plastic sextant.
When conditions are really bad, there is usually too much cloud cover for astro to be counted on anyway.
Fortunately, when you are on the open sea and only doing five or six knots, missing a day's noon sight or even sights for 48 hours (not unusual), is unlikely to mean 'game over'. Pre GPS, it was normal to go to DR for as long as it took and most of us stayed out of trouble simply by being conservative and staying well offshore.
Five, ten or even 15 miles will normally get you in sight of land, when navigation switches to 'pilotage'. Here, the sextant is still useful for measuring distances off landmarks, lighthouses etc. And surprisingly accurate - easily to within half a mile - which of course you need close in to obstacles. Boats and ships rarely come to harm in the open sea - most wrecks occur within sight of land.