I earned $5000 stipend from the REU program at UNT (University of North Texas), which also happens to be my total income for 2019.How do I include that in my 2019 taxes?

That depends on whether you have offsetting Education Expenses or not.

Click this link for detailed info on How to Report Stipend Income in either case. 

 In 2019, you do not need to file a tax return if all of the following are true:

• Under age 65
• Single
• Don't have any special circumstances that require you to file (like self-employment income)
• Earn less than $12,200 (which is the 2019 standard deduction for a single taxpayer)

However,  If there were taxes withheld it would be to their advantage to file for the refund.  Be sure that they show that someone else CAN claim them as a dependent.

From <Who Must File>