What is known from the order of events
Rachel bare Joseph in Padan-aram. Benjamin was born later, on the way to Ephrath (Bethlehem), and Rachel died in childbirth. Genesis 35 records that birth before Genesis 37 describes Joseph at seventeen and his sale into Egypt.
Therefore Benjamin was born after Joseph (Jacob about 91 at Joseph’s birth) and before Joseph’s sale (Jacob about 108). That yields a window of about seventeen years.
Why a single number is not forced
Unlike Jacob’s death (147) or entry into Egypt (130), Benjamin’s birth has no age formula attached. Estimates that assign Jacob a precise age such as 100 or 106 go beyond what the text requires.
What can be said safely is that Jacob was already advanced in years—well past his marriages at about 84—and that Benjamin was the youngest son, born after the family had returned toward Canaan.
Related ages
Joseph was older than Benjamin by some years within that window. When the family entered Egypt, Joseph was about 39 and Benjamin was an adult with sons listed in Genesis 46. For Benjamin’s age at the migration, see the dedicated article.