Talking about 5.000 km is hard: While it won't get you from London to New York without some post-crash landing swimming, the current largest electric plane can fly ~100 miles at around 114mph, with 9 passagers.

I see that you take the laws of physics into account, but allow me to state this for the sake of the conversation: In order to replace jet fuel, we must match what we could call it's useful energy density (energy/kg * efficiency). While electric engines are probably more efficient, we're still up to 2 orders of magnitude away – that's requires a 50-100x improvement of energy density, while maintaining the needed high discharge characteristics, developing a sufficiently efficient electric jet engine and taking into account the increased weight. All at a price where people won't need to save up for years, in order to visit their families.

While I hope to see a zero emission future in my lifetime (actually a negative-emissions might be needed for at time), I feel like putting batteries into airplanes is a bit too much "Silicon Valley Sophism" – shoving the same solution at each and every problem, rather than figuring out what the core of the problem is.

I do love electric cars, but they are not for everyone('s budget). Perhaps the solution is synthetic fuels, combined with carbon capture and a cheap, clean and reliable energy source, such as nuclear power. I know this isn't exactly cheap or readily available either, but it seems like one would bypass a lot of the issues above, by focusing on the source of the problem: Non-neutral use of carbon fuels.