This seems to be a horribly pessimistic projection, Ian, and I hope that you are wrong. But ....
Arguably, the US has performed abysmally in the managing of the covid epidemic and their cumulative infection rate is now 11.5% - but still rising! Will it peak at, say, 15% - who knows?
But if 80% vaccination rate is achieved and the vaccine is 60% effective against the delta strain and there is a "natural infection rate of 15% then we run the numbers:
- Unvaccinated: 20% of population, 15% infection rate => 3% infected.
- Vaccinated: 80% population, 60% imune, 40% exposed, 15% infection rate => 4.8% infected. [80*(1-0.6)*0.15]
Your 5% is then not unrealistic.
But if the vaccine effectiveness is actually 90% then the infection rate for the vaccinated drops to about 1.2%. Time will tell.