If am not wrong (still learning Swedish), it has to be "Jag har inte sett dig på fem år."
On my grammar pages to distinguish between "på" and "i", it is written that 'på' is used in following cases "Hur länge har man inte gjort något?", "Hur länge ska man inte göra något?"
I am hopping that helps you.
på with time expressions like this is used for accomplishing things. So it makes sense to say you read an article på en kvart or that the kids, say, built a snowman or made a sand castle på en kvart. But leka doesn't have any kind of result in it, so it doesn't make sense together with a time expression like that.
The negation doesn't change it per se. Jag kan inte läsa artikeln på en kvart 'I can't read the article in 15 minutes' or Jag vill inte hålla på med det här i en kvart 'I don't want to be doing this for 15 minutes'.
There are lots of different time expressions and there are (at least) two dimensions to it. One is that i is used with some nouns and på with others. The other is that for nouns that can be used with both i and på, the meaning changes depending on which preposition you use.
inte på länge (you have a typo in your sentence, it should say Vi har inte setts på länge 'We haven't seen each other in a long time') is a sort of set expression which usually appears with a negation, this was probably what your teacher was telling you.
länge is never used with the preposition i.
Can someone use i, på, om, till, and tills in a basic worded complete sentence. In the following sentence, can someone use innan, före, efter, and under (the during meaning) also in a basic worded complete sentence. Please keep in mind that I am looking to grasp the conceptual meaning of the words in context. In summary,
Sentence 1: i, på, om, till, and tills
Sentence 2: innan, före, efter, and under (the during meaning)
You know how English has a word for "sixty minutes" - "hour", that is.
Now, if you want to say that the children play for sixty minutes, you say "for an hour", not just "for hour".
It's the same in Swedish but Swedish also uses kvart for "fifteen minutes" in the same way that we use timme for "sixty minutes". So then you need the article because the amount has been turned into a noun.