Your school may not do the federal or state withholdings for you, and they have to do the social security and medicare withholdings. You can make some estimates payment now to IRS and FTB.

You don't have to pay penalty until your tax balance due is over than $1000. Now, you have $5000 gross income, you have a high chance of more than $1000 tax due, so please contact the authorities to make payments once you talk with your school.