Your conclusion is correct that if you've "used up" your 5 full years of being an "exempt" person from the Substantial Presence Test, per your international student visa status, then in your 6th year living in the United States you would be considered a resident alien for US tax purposes. In other words you would no longer be an "exempt" person, if you otherwise met the days present requirement of the Substantial Presence Test, as explained at the following IRS webpage:
That said, scholarship income received that is in excess of the cost of university tuition and fees is considered taxable income to US citizens and resident aliens. It does not matter if the scholarship source(s) is foreign or domestic to the US. It is still taxable income, to the extent just described.
Thus, you will need to determine if the amount of (excess) scholarship income totals up to a "large enough" amount that requires you to file a federal (and / or state) income tax return. For an answer to the federal question on the need to file (or not), you can look to the materials found on Pages 3, 4, and 5 of IRS Publication 501 here:
Alternatively, you can use the web-based IRS tool (Do I need to file a tax return?) available at this webpage:
If you determine that you don't need to file a tax return at all (because your taxable scholarship income is not large enough) then basically you are done. Form 8843 is only applicable where you can claim to be an "exempt" person for your first 5 years studying in the US, or if you have a serious medical condition that would prevent you from leaving the US. It therefore does not need to be filed once you reach resident alien tax status.
If you determine that you need to file a tax return, then as a resident alien you will use the Form 1040 (1040A, 1040EZ) series, and not the Form 1040NR (1040NR-EZ) series for nonresidents. And for information on how to include and report taxable scholarship income on a US tax return, you can read the following AnswerXchange post:
Although the discussion at the post (link) above was originally for a graduate student, the same principles of taxable scholarship income (including grants and stipends) would equally apply to your situation as well . . . at least with respect as to how to report and enter any (taxable) scholarship income not used to pay for tuition and fees.