Educational Opportunity and Success Act of 2019 This bill reauthorizes through FY2025 and revises TRIO programs. (These outreach and student-services programs identify and provide services to students from disadvantaged backgrounds.) Among other revisions to the programs, the bill prohibits the Department of Education (ED) from rejecting TRIO grant applications based on certain errors, requires ED to provide additional technical assistance to interested grant applicants, and allows program administrators to use a student's most recent Free Application for Federal Student Aid to determine TRIO program eligibility.