The 5 courses are required to apply to Mays as a transfer. Your gpa is solid and you’ll need to keep it about a 3.8. They only take 100 external students per year (not semester). They most likely won’t even review your application because you have to clear the bar first then they look at everything else. Anything done in high school is irrelevant.
My advice is take math 1 in wintermester if available. And then 2nd math in spring. Take speech in spring as well. Then apply in the spring for the fall. They will defer you for grades most likely and then review your application again right after spring grades are released. How many credits do you have completed right now (not including this semester).