The phrase in parentheses is explaining that he wants a burger and not to have sexual relations with 5 men. It acts as an “anti” circle like the anti sea bear circle in the SpongeBob episode. So using the phrase to communicate that he wants a burger and not hot steamy man on man on man on man on man on man sex, clarifies to the reader that the author is not gay.
Sounds like you want sexual relations with five men.
The image shows a reference to the sea bear episode of SpongeBob. Sea bears refuse to go into sea bear circles. The joke is that even just specifically saying "the burger chain" in parentheses is enough to keep bears (big bay men) at bay.