I have unused fed/prov tuition and education amounts from 2017. I'm longer a student and was not a student in 2018. I worked full time in 2018. Can I claim these?

If you need them to reduce your tax owing to zero, absolutely!. Actually, if you have unused tuition credits, you must use them to reduce your tax owing. 

Enter your unused amounts in the Student section of your return.

CRA My account confirms I have $23891 in Federal and $15726 in Provincial amounts available. These two amounts are autofilled into TurboTax. However,  upon completion of the tax return a Red Flag audit alert pops up and indicates tuition amount exceeding $5000. Have I incorrectly completed this section of my tax return?

It's just a warning to go back and check your entries. Since there have been numerous cases of students misplacing zeros, the warning was added just as a reminder to ensure the amounts are correct. If yours are accurate, you can ignore the warning.