They have different meanings: Year 5 is not the same as fifth form. A year 5 pupil is nine or ten; a 5th form pupil is fifteen or sixteen. Year 5 refers to the current state school system in England and Wales*, which begins in Year 1 when children are five years old and covers both primary and secondary school education. Year 5 is the penultimate year of primary education, when children are nine and ten years old. 'Fifth form' refers to a previous system for naming years in secondary schools. The form system is no longer used in state schools in England and Wales, but it is still used in some private schools. Fifth form used to be the last year of compulsory school, ending when students were 16 years old. They would then either leave school, go to a different establishment ( e.g. training college) or move up to sixth form to study for A levels. Even though the first to fifth forms effectively no longer exist in state education, the term 'sixth form' and 'sixth form college' are still used, and secondary schools sometimes still refer to the students' "home room" teacher as 'form teacher' and their home room group as 'form'. * Note that this only applies to England and Wales, not the whole of the UK. Scotland and Northern Ireland have their own systems.

Thank you so much for the great explanation, Julia! So, do the example sentences that you gave only refer to the two final years of secondary school? I mean, it wouldn't make any sense if I said: 'You're not old enough to drink, you're only in 5th/7th/8th, etc form?' or 'Do you go to this school? Yes, I'm in the 5th/7th/8th, etc form?', right?

It's not common at all... with one exception. Generally 'form' would mean an individual tutor group: "I'm in Mister Smith's form" - although that is only in some schools and isn't widely used. As you say, 'year five' would be the more widely recognised age group (and for what it's worth, year five is ages 9 - 10). The exception is "sixth form" and you wouldn't necessarily use a definite article as it's quite colloquial. Sixth form is the A-Level years, so GCSEs are usually taken in the school year you turn 16, sixth form is then generally ages 16-18 - two school years of study. The correct term for this is 'Further Education' (post-GCSE study). "Where are you going for sixth form?" / "You're not old enough to drink, you're only in sixth form" but also "Do you go to this school?" "Yes, I'm in the sixth form."

Form means registration class, the first class of the day