As a supporting datapoint, in the entire company I work at, there isn't a single standup with that many people.
A couple of questions Was the company you work at a software product company? Are your teams cross functional? Do people exist across multiple teams?
My fundamental issue with splitting a 15 person team into three 5 person teams it seems more difficult to satisfy two other attributes I think are valuable in teams. That they are cross functional and flat.
Where I work it is all software. We can and sometimes do have folks on multiple teams but generally try to avoid that. And teams can definitely be cross-functional.
how many of those 15 ppl care about what you are doing on a regular basis. I am guessing not more than 5. I've never been in a standup with more than 5-6 people, 15 ppl standup sounds too ridiculous to me.