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The number "5" expressed in binary is "101". Counting all the "main" games, Fallout 3 was the fifth game in the series Fallout 4 is the seventh.
Fallout 3 began in Vault 101 Fallout 4 begins in Vault 111. Even the implied military background allows for several technical degrees and experience setting up electricity and basic living in the wilderness, which is sure to come in handy in the new level editor. The new, broader and far more extensive crafting options exist because this protagonist actually went through a classical education. A near-hit would provide a plausible (at least in-universe) reason for the Pitt's conditions. Alternatively, given the Fallout timeline's branch from our own, Pittsburgh makes a very reasonable target as it was a major center of steel production for quite some time. Though it's far more likely Philadelphia was hit, as the Pitt is relatively untouched. New York is an obvious target for the bombings, but Pennsylvania has particular significance to Fallout fans: it contains Pittsburgh - eventually, The Pitt. The opening newscast specifically mentions nuclear detonations taking place in New York and Pennsylvania. The rocket shaped bottle was part of a promotion, should the gamer find some of the advertising notes from the bottling company. It's also no wonder kids mistake the Isotope liquid in Rocket Souvenirs for Nuka-Cola when its glasses are shaped like that. Send a nuke into your mouth for an explosion of flavor. Nuka-Cola now comes in a rocket bottle. The only way you can be farther off the map is by going out of bounds or teleporting to QASmoke, which removes you from the map entirely. Not only is he literally off the map, he's literally off the grid as well. Goes even further if you take the gridlines on the map into account. If you look on the Pip-Boy, his location is outside the dotted line. Virgil's already made it clear that he's using the Glowing Sea's radiation to hide, but there's another reason he's doing so well keeping hidden. The song is "It's All Over But the Crying" by the Ink Spots. In the prologue during the character creation part there's a song playing in the background. Of course he would have that one as the first voiced Fallout protagonist, he surely is more charismatic than the previous PCs. 111 has the Charisma Bobblehead in his home. Bethesda waited seven years to execute this. In Fallout 4, you get an achievement named ".The Harder They Fall" for killing five giant creatures in the Commonwealth. In Fallout 3, you get an achievement named "The Bigger They Are." for killing all five Super Mutant Behemoths in the Capital Wasteland.