1. Most foreigners don't get a "tourist
visa". Places like India do, I believe. Americans, for example, get what is called a visa
waiver. It lasts 90 days.
What is your nationality?
2. You started the conversation by saying: my visa (temporary visitor) is from March 15 to May 15. But your most recent post contradicts that by saying: my visa is from Feb to May 15, 90 days. The first one is a period of only 60 days, which does not make sense for a visa waiver.
Which is it?
3. Your main problem:
I didn't realize the expiration of my visa is on the 15th on May. Am I going to break the law? Should I reschedule my flight?
Yes, you are going to be breaking the law. Even one day over your visa/waiver is against immigration law.
You might not get caught, or as you pass through immigration on your way out, you
might. That would be a minor hassle at best (probably a stern talking to) or something major at most (20 days of incarceration, a fine, maybe even being blacklisted from returning here for 1-5 years). During those 20 days you could be interrogated without a lawyer daily.
Here's what happened to some students who overstayed a short time.
Change your flight, or leave and come back as mentioned above, or if you don't want to do either of those, go to an immigration office and beg forgiveness ASAP. I still think they will tell you that as long as you're still here legally, you should leave before the deadline, but who knows if they will extend your stay long enough? Usually, that is granted only if you can state a very plausible reason and show you have enough funds. Being unaware of what's written on your passport is
not a good reason, usually. Certain nationalities might make things worse.