Yes, you can file 5 state tax returns for the same state. The federal return and the state return are e-filed at the same time. Or the federal return can be e-filed first and the state return e-filed after the federal return has been e-filed and accepted by the IRS.
A state return can only be printed and mailed if the federal return is not e-filed.
After the 5 federal e-files have been used then all other tax returns must be printed and mailed.