When does the 5 year timeframe to claim the R&D Credit against my payroll taxes begin?

It starts as soon as soon as your company has any gross receipts at all - even interest that might be earned from a bank account.

If your company changes structure, like with a new EIN, it will likely not reset the timer. As long as your business is still doing the same thing, it’ll be considered the same business. See the “trade or business” definition from the IRS for additional details.

If you’ve had any other company structure changes (ie. acquiring another company, another company acquiring your business, etc.), your ability to claim the credit against your payroll taxes may change based on the other company's gross receipts information.