Will there come a time when every melodic combination of 5 notes will have been used to start a tune?

If you limit the notes to a 2 octave range, which should be more than enough, and allow each note to be quarter, half or whole, that gives about 250 million possibilities.

Suppose that all these note combinations were programmed into a computer and we divided them among 25,000 musicians. Then each musician would need to listen to 10,000 of these note combinations to go through all of them. Even allowing for only 3 per day, it would only take about 10 years to go through them all. Would the musicians be capable of telling which ones could conceivably be the start of a song?