I reckon you are 4th cousins once removed. I worked it out this way:
My grandmother and great-aunt were sisters
Next generation on both sides was my mum and her 1st cousin (descended from mother and aunt)
Next generation is me and my 2nd cousin (descended from grandmother and my great-aunt)
Next generation is my child and her 3rd cousin (great grandmother and great great-aunt)
Next generation is my grandchild and her 4th cousin (2 x great grandmother and 2 x great great-aunt)
You have another "great" (3 x great grandmother) so your parent is at the level above .... 4th cousin to your friend. As you are another generation further down, that makes you and your friend 4th cousins once removed.
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Two ancestral lines, with children below parent, and your 3rd great grandmother's relation to the person on the right:
Generation 1: Your 3rd great grandmother and her sibling = siblings
Generation 2: one of your 2nd great grand parents and child of sibling = 1st cousins (aunt)
Generation 3: one of your great grand parents and grand child of sibling = 2nd cousins (1st great aunt)
Generation 4: one of your grand parents and 1st grand child of sibling = 3rd cousins (2nd great aunt)
Generation 5: one of your parents and 2nd grand child of sibling = 4th cousins (3rd great aunt)
Generation 6: You and future child of friend = 5th cousins
Your friend is " 2nd grand child of sibling" in Generation 5, and 4th cousin to one of your parents.
When he has children, they will be your 5th cousins.
This would be WAY clearer if you'd copy it off and put in the real names.
I reckon you are 4th cousins once removed. I worked it out this way:
My grandmother and great-aunt were sisters
Next generation on both sides was my mum and her 1st cousin (descended from mother and aunt)
Next generation is me and my 2nd cousin (descended from grandmother and my great-aunt)
Next generation is my child and her 3rd cousin (great grandmother and great great-aunt)
Next generation is my grandchild and her 4th cousin (2 x great grandmother and 2 x great great-aunt)
You have another "great" (3 x great grandmother) so your parent is at the level above .... 4th cousin to your friend. As you are another generation further down, that makes you and your friend 4th cousins once removed.