Can you provide the source for that quote? 5 billion years seems way too soon.
The Hubble constant is currently approximately one doubling per 14 billion years [1]. So 5 billion years isn't enough to double the recession speeds. AFAIK there's plenty of galaxies receding at less than half the speed of light. Wikipedia estimates 150 billion years (6000x expansion) for all but the local group to be beyond the horizon [2]. So your quote seems to be off by two orders of magnitude.
The Hubble constant is currently approximately one doubling per 14 billion years [1]. So 5 billion years isn't enough to double the recession speeds. AFAIK there's plenty of galaxies receding at less than half the speed of light. Wikipedia estimates 150 billion years (6000x expansion) for all but the local group to be beyond the horizon [2]. So your quote seems to be off by two orders of magnitude.
[1]: https://astronomy.stackexchange.com/questions/49248/interpre...
[2]: https://en.wikipedia.org/wiki/Timeline_of_the_far_future