I don't like the term "gifted" and wouldn't describe my 5 year old dd as such, but her school does.
I am assuming that your question refers to the point at which this was picked up at school, rather than the point at which we, as parents, realised that she was quite bright?
DD is currently in year 1 at a state school, and her reception teacher first said that she thought she was "gifted" after about half a term in reception - at our first parents' evening. At the end of the year, they asked us to consider letting her skip year 1 and go straight into year 2, but we declined. I am not entirely sure what exactly makes her "gifted" in the eyes of the school, because I have never thought to ask
, but at various points in reception and year 1, her teachers have mentioned the following:
1)Very advanced reading skills for her age (not just decoding but comprehension and expression as well)
2)Advanced numeracy skills for her age (this first emerged early in reception when they were making repeating patterns and dd was able to create and describe very complex ones, but now seems to relate to her understanding of shape and space, her mental maths, and her ability to apply mathematical knowledge to real-life problems etc)
3)Very good general knowledge across a wide range of topics - knows lots of random facts that a five year-old usually wouldn't! 
4)Asks "startling questions" and shows a high level of intellectual curiosity
5)Is "unusually perceptive" and has a talent for empathising with others' feelings.