As far as I can tell from the websites of the Foreign & Commonwealth Office and of the Turkish Consulate, children require their own visas. (That's common practice across most countries). For a definitive answer, phone the Consulate on 020 7591 6900.
The £10 'pay on entry' fee is a special concessionary rate to citizens of the EU and USA. The full fee (which is what you'd pay if you got your visa from the Consulate, and what non-EU/US citizens have to pay) is £68. So perhaps a tenner for a 5-year-old's visa doesn't sound quite so bad after all?
Chris