5 months, 4 negative pregnanc tests and no period? What could this be? Could pregnancy still be possible?

Amenorrhea. There are many reasons to explain missed periods. If not already done, a blood pregnancy test would confidently rule out pregnancy. Additionally, some other blood tests to consider would be hormone levels, estrogen, fsh, lh, prolactin, TSH as well as adrenal and testosteone testing. A physical exam should also be done to look for signs like hirsutism which could indicate things like pcos.