In most cases, small-business credit cards will not add to your Chase 5/24 count because they don't appear on your personal credit report. This actually includes Chase business credit cards, as well. So if you're at 4/24 (four credits cards opened in the past 24 months) and you open the Ink Cash card, you'll still be under 5/24 even though you just opened a Chase card.
However, if you open a business card with Discover or Capital One, that account will be reported to your personal credit report and will add to your Chase 5/24 total.