魯哀公 Duke Ai of Lu (r. 494 to 467). Numerous Analects feature Duke Ai talking with Confucius or disciples (2.19, 3.21, 6.3, 12.9, 14.21). Real power in Lu lay with the Three Huan Families, 季孫 Jisun, 孟孫 Mengsun, and 叔孫 Shusun, so that the Duke was more or less of a figurehead. Though Confucius and his students, notably Zilu, favored returning power to the Duke, their relationship in the Analects does not appear to be particularly close or substantial.
Why does Zhuangzi pick Duke Ai for the conversation with Confucius in 5:04? Given the sparse evidence we have for a relationship between the two men, it is likely Zhuangzi was relying on other sources that are lost to us. Duke Ai appears in 9:04, where appears to be someone who is drawn to Confucianism but doesn't really get it: he mistakes the form for the substance, though, admittedly, Confucius is frequently depicted this way in Zhuangzi, as well.