$42,000 in Student Loans, growing to $120,000 in 3 years, paying off $800 a month for now, what's next? Hello,

To make long story short, I am debt free with my first job out of college but my significant other is currently in graduate school with $42,000 in student loans. This will grow to $120,000 in 3 years. 

$82,000 of the $120,000 will most likely be unsubsidized loans that accrue interest all the time, while the rest have a grace period of a few months after graduating. The unsub loans also have higher interest rates.

With my current job, we can realistically pay off $600-800 from the highest interest loans after all monthly expenses. My main question is regarding the $10,000 we have saved up between us. We plan on putting away $5000 as emergency fund. Should we use the other $5000 to pay off the unsub loan or invest it?

Thanks in advance