Yes, good lord, you can't even safely RUN a 250w heatlamp in that space and have it safely away from combustibles
I don't know what your weather is like, that will considerably affect what wattage you need; but I would suggest starting with a 100w regular lightbulb and see how they behave with that, then you can swap to higher or lower wattages as needed.
(And/or install a second socket and use two lower-wattage bulbs -- it is not quite so much an issue with older chicks like yours, but there is a LOT to be said for having two half-the-wattage bulbs as opposed to one higher-wattage one, first because of fire safety and second [and biggest] because that way if one of them goes dead the chicks will still have *some* heat from the other bulb)
The way to tell if you've got the right wattage (and/or right distance from the chicks) is that you want them, when they are resting rather than exploring, to be not off in the far corner of the coop, not right directly under the bulb, but a short ways out, sort of if you imagine a cone projecting down from the bulb you'd want them around the rim of the cone. That means they have both too-hot and too-cool areas available to them, so can thermoregulate just by moving around as needed.
I would not leave the popdoor open overnight on 5 wk old chicks, for several reasons (you don't want them starting a habit of sleeping outdoors, and you don't want cold breezes coming in at night when you cannot check on them and realize they're too cold and do something about it). When they are older and fully feathered, it is "ok" to leave your run open all night as long as you realize that it is MUCH MUCH more common for people to be *convinced* their run is 100% predatorproof than for it to actually BE 100% predatorproof, with the result that doin' that not-infrequently leads to you not having any chickens anymore one fine morning. Go browse the Predators and Pests section of the forum, see how many 'something ate all my chickens last night' threads involve people who were just SURE nothing could get in. So as long as you understand that, it's your choice, everyone has their own ideas of risk tolerance and so forth.
Good luck, have fun,
Pat