I would contend that a 5-year-old has general intelligence, and therefore an AI system with the language and reasoning abilities of a 5-year-old has artificial general intelligence.
But the discriminator of having to "pay an intelligent professional otherwise" sets the bar very high. That implies AGI must be an expert in every subject, surpassing the average human. I'd prefer we use a different term for that, like "artificial superintelligence."