The spell says "Any spell of 5th level or lower cast from outside the barrier can't affect creatures or objects within it", but it doesn't outright specify whether spells can pass from inside to outside, such as if the caster of the globe were to use Flame Bolt. I've been assuming for ten years, since this spell appeared in 3rd/3.5 that, yes, the person inside can cast spells against people outside, but as this is a new edition (and I am DMing our inaugural campaign in it), I thought it prudent to make sure in case my players come up with the same question.