Mad Professor?

This problem is from the website of Prof. Martin Deraux. Mad Professor?

A professor tells her assistant that she dined with three people last night. She also tells him that the sum of the three people’s ages is twice the assistant’s age and that the product of the three people’s ages is 2,450. Then, she asks him to tell her the ages of the three people. After a while, the assistant tells the professor that he doesn’t have enough information to solve the problem. She agrees and says that she is older than all three people with whom she dined. The assistant, who knows her age, promptly gives the professor the correct ages. The question is: What are the ages of all five people in this story?