$5500 in solar panels including a battery would be just enough to keep the AC on all summer, and that's being fairly high on the temperature, around 26.
So based on cost alone and not power draw, with the AC off you could comfortably power a fridge, PC, and water heater, I guess? But I'm talking out my ass here
The issue is winter: It gets down to -25c and there is very little sun (not that it would help due to snow on the panels). In January and February this year I generated a grand total of 5kWh :D
However my house is a new house, it's designed to modern building standards and has 30cm of PIR insulation in the walls and even more in the roof. There's just no way to properly renovate old buildings to be like that without basically rebuilding the whole thing. The actual cost of materials is not expensive though (for the west). In milder climates (UK I'm looking at you) there's really no reason all new houses cannot be net-zero.
Meanwhile, we have, in Europe a lot of buildings from late 19, early 20th century that are perfectly habitable today and often are ruined by modern standards that not respect old standards. For example basement addition that prevents the apartments from “breathing” and causes them to become damp.
https://en.wikipedia.org/wiki/Solar_power_at_the_White_House...
It is also true that solar water heating has unpleasant failure modes.