I am not married, but have been living with my boyfriend for about 5 months, his grandfather is on his death bed. If his grandfather passes, legally how many days does our employer have to give us to grieve. We work for the same company.

They really don't have to give bereavement leave, at least that's the way I see it. Your s/o will have to take leave as he sees fit.

Legally an employer is not required to offer ANY bereavement leave. If there is nothing spelled out in the employee handbook, then its at the discretion of the employer. Generally an employer will allow 3-5 days for members of the immediate family and 1 for others.

Living with your boyfriend for 5 months doesn't make you a member of the immediate family.

Assuming you are in the US, there is no legal requirement to give any pay for this. Most companies as noted will give him 4 to 5 days. Some companies have written policies for this.
There is no common law in most US states, and esp not after merely 5 months. So there is not normally ANY days approved even in company policies in the US. They may or may not give you some days.

Unless there is a formal policy the days are normally always non paid days off.