I got my green card this year. I left the US for 37 days and came back. Now in December I wish to leave the US for five and a half months, approximately 175 to 170 days, which is less than six months. Can I go for this duration? Will my previous 37 days be added to this, which would make my absence more than 6 months total?
According to this page from the US Customs and Border Patrol, you can stay out of the US for up to a year before you run into problems.
(I found other, non-authoritative, sites which suggest you may be subject to additional questioning between six months and a year.)
I think you will be fine.