No, there is no formula quite that simple while we're still in the transient, exponential growth stage for omicron. 5x transmissibility can lead to single-day infections much greater than past peaks. If omicron does cause a disaster in the US and other western countries, it will probably be due to a short (2-3 week) window of insanely high daily case rates, leading to very high daily hospitalization/ICU requirements. If the US hits let's say 1M confirmed cases/day for example (3x the peak last winter), with a daily demand for beds (non-icu) of ~25k, things would get very bad in urban centers. The combo of exponential growth and localized hospital resource constraints means that what would seem at face value to be an even tradeoff of transmissibility for lethality is not so simple.

Omicron might be a blessing in disguise, but there is a very bad plausible outcome for the coming month.

Not if you factor time into that math. 5x more infectious on the first cycle means just 5 times the infections, and equal hospitalizations, but the next cycle all of those 5x the number of people spread it again to 5x the number of people. So even though it's 5x milder, you've still got 5x the people showing up in the hospital. It gets worse and worse the more cycles you go. 25x in hospital, 125x in hospital, etc. You run into mitigating factors in real life, as the entire population is consumed, but that's a super steep slope comparative to the baseline.