Can someone get very ill or die from taking 5 puffs of inhaler when the recommended dose is 2?

Inhaler: Unlikely. An albuterol inhaler or beta agonist will make someone's heart race, a steroid inhaler would very likely cause no side effects (just was mouth out to avoid a yeast infection).

Unlikely ...however.: I recall at least one case of a model using an inhaler to stave off hunger that died when the drug sent her heart into a faulty rhythm. If you are not getting results after 2 you should be calling or going in for urgent care. You may need intravenous steroids & other care.