"The night of the 5th" would be 2000-2359. After that, it's the (early) morning of the 6th.

I get ya, though.

If you want a more confusing one, which months belong to which seasons? Most people seem to think winter (at least in the Northern hemisphere) is December through January. We are certainly in the winter now, and it's December. Ergo, December is a winter month, right? Christmas is a winter holiday, right? Yes, but also no. The first day of winter is the winter solstice, December 21. So 10 days of December are winter, but 21 days are autumn. (And Christmas, as it's celebrated today, just hijacked the winter solstice to bring Christianity to pagans.) So when people say the weather is changing, it's warm in December... yeah no shit! The first 3 weeks of it are autumn, and autumn is not necessarily cold!

If people thought of Winter as January through March, Spring as April through June, Summer as July through September, and Autumn as October through December, people wouldn't trip about seasons feeling longer or shorter, because they'd be attributing the correct months to the seasons. Of course, since seasons are based on solstices and not the months, it's more accurate to say Winter is the first quarter of the year following the Winter Solstice (which is a better year end/beginning), Spring is the second quarter of the year leading up to the Summer Solstice, Summer is the third quarter of the year following the Summer Solstice (which should be celebrated as well), and Autumn is the fourth quarter of the year leading up to the Winter Solstice.

Time is really only funny because the terms we made up to define them are not perfect. You would prefer the day begin with sunrise, and end when the night ends. That makes sense, to a point. I know some pagan cultures measured months by the moon cycle, so it's not unreasonable.