2000 Civic. Seat belt got caught in door, and I just never had a reason to look back. I wonder because I think it’s been a while since the battery was changed, and I’ve got a new job now and little time to get it checked. I’ve got a little over a month to go before my next service appointment.
Estimates would be nice, at least so I can tell whether this is anything significant or not. Thanks!
With an otherwise more or less healthy battery and a normal bulb, this should be no big deal.
Does the car start?
If the car starts, take it out for a drive to re-charge the battery.
As others said, if you could start it, it’s fine (and at the time, probably should have let it run for a little while). Never give it another thought.
Was the light really still on 5 hours later? I thought most of the electronics (including the dome lights) turned themselves off after 20 minutes or so to prevent killing the battery. I stopped lugging around jumper cables at least 15 years for just this reason. When people ask me (friends, not random people on the street) if I have them I usually mention that I can’t think of the last time I killed a battery. Before that, using the dome light after you got home almost always meant needing a jump in the morning.
It was on because the door was stuck opened. Most cars have a switch on the light that will allow it to stay on as long as the door is opened, or go off after five minutes or so, even if the door is opened. If there is not switch, then the default is usually for the light to stay on. You have the same choice with you headlights. You might want your headlight on when the car is off-- or off when the car is on, so you can flip a switch. However, the choice most dealers set all cars to is “Auto,” which means the lights come on when the car is on, day or night, and go off about 60 seconds after the car is shut off. Dealers usually set the dome light to go off if the door is opened, but some set them to remain on, and then, the owner can always change them. But, then if this car (and it is 17 years old) did not have the option of the dome light shutting off, well, then it didn’t have the option.
But as others have said, if it started, don’t worry. It would have been a good idea to take it out on the highway for 15 or 20 minutes-- worst idea would be a very short trip, in-town trip.
The OP can check the battery with a multimeter (it should read a little above 13V-- it will probably start at as low as 11, though; if it reads less than 12.6, you need to take it for a drive), or take it to an auto parts store-- they often perform battery checks for free.
One thing-- make sure everything is off when you start it, so nothing but the starter is drawing. Turn off the radio, and the lights, if they are on auto.
Estimate: About 5 hours worth. 
How long of a drive is it to work? If the charging system on the car is working well and the battery isn’t very old (holds a charge well), you’ll be able to recharge it through normal driving. There is nothing that a shop will do for you except possibly test the battery and hook it up to a trickle charger overnight. I’ve had a battery deep cycle charged (re-conditioned?) when it was under warranty. Turned out it was defective and it was replaced.
if you knew the wattage of the bulb in question, you could estimate the current draw and then figure out how much of your battery’s ampere-hour (Ah) capacity it used.
so just some rough estimates; a dome light bulb is about 10-12 watts, which means it draws about 0.8 amps when lit. A car battery (in good condition) has about 40-50 amp-hours of capacity. So basically, you’d have to leave that light on for about 50 hrs continuous to completely run the battery down. So if the light was on for 5 hours, you ran the battery down about 10-20% at the most, and a 20 minute drive is more than enough to bring it back up to the charge it can hold.