Had the exact same problem and was able to solve it by first going to the “Twinmotion” tab and clicking “Install” for that. After a short time I went back to the “Library” tab and UE5 appeared (and the “Install Engine” button extended to include “Unreal Engine 5.0.0”).
There was suddenly an additional install entry called “Quixel Bridge”, which I assume is the Twinmotion thing (or a requirement for it), which I canceled, and now I’m installing UE5. 