Your 5th accountant was being nice. Even IF your PTO was operating under the wing of the school, I suspect the school doesn't know about your $$ (as far as its own tax reporting goes). Anyway, you indicate your PTO is separate from the school. First of all, don't panic. They're right, you shouldn't remain unknown to the IRS, but the IRS police are not out looking for you.
Like Pals said, the first "test" is whether your PTO is banking all this money under its own tax id number or the school's (or God forbid, someone's personal social security number). That's important to know. Call the bank and find out what identification number was used to set up the account. If your $$ is under the school's number, you are technically raising $ for the school and the 5th accountant is maybe correct. If the $$ is under your own #, then the other 4 are right, but you need more than a quick reply about needing to file forms. If the $$ is under a ss#, then you need to get your own PTO's tax id number from the IRS, open a new small business account with that number, and transfer the $$ to the new account.
I should clarify that I am not an accountant. But I know there are specialist accountants who work primarily with non-profit groups, and there are lots of other accountants who don't. A quick answer from a non-specialist won't help you much. Lots of PTOs have evolved from exactly your position (loads of $, not incorporated, not 501c3) to be formally established as a federally-registered non-profit corporation. It's not rocket-science but it does require your group to make some important commitments:
1. You must accept that once you are incorporated and 501c3 that your group will forever properly file the annual paperwork required by your state and the IRS. Heavy fines if that is ignored.
2. You must accept that the process to initially file for 501c3 is fairly tedious, and will cost your group $500 in filing fees. You don't need to hire anyone to do it for you, but you need to find a volunteer who is comfortable digging through the application and completing the process.
Typically, the first step is to incorporate in your state. That's easy and usually cheap (less than $50). Then you file for 501c3 with the IRS using form 1023. The good news is that the IRS views your creation date as the date you incorporated so you can fill out the application from the viewpoint of a brand new org and not have to dig up your financial history. It's still a lengthy application, but that makes it a bit easier.
Yes, with $$ like yours, you should formalize your group. Take time to read through other posts on this site, contact the IRS with your questions, and maybe you can find a 6th pro bono accountant who has in depth experience with 501c3 registration. I also suggest you purchase the Getting Started guide from this site - it includes detailed instructions for filing out the paperwork from the eyes of a PTO.