2005 Explorer. Dead battery and no door key

If your talking car battery being dead, sometimes, you can use battery charger at starter motor bat terminal in order to charge vehicle battery. I haven't looked, so I don't know how hard it is to get at starter motor? As far as driver side door, you can call a locksmith to open it. Yeah, it will cost you, I guess it just depends if you think the cost is worth it?

I believe that 05 does use the same key for door and ignition. Should work for opening, and alarm shouldn't go off since your battery is dead. The battery for the key fob is easy to replace if that is the battery you are talking about. The regular battery can be charged by a proper charger, jumped off by a good battery, or replaced once you gain access. Remember red goes to + and black goes to -.