You've completely misunderstood how the multiverse functions in Type-Moon.

Fate/strange fake is it's own reality where a budget Grail got made in the US. The Moon Cell does not exist in most realities, and it is actually impossible for the Moon Cell HGW to take place in the same reality as F/SN, due to it being based in a world where the Aylesbury Ritual fucked up magic in the 70s. Unless you're referring to Apocrypha, which is a very very bad gauge of Holy Grail Wars, then I'm not sure where you're drawing your information. They are separate instances, not to be viewed as a whole. The OP as much mentions the 5th Holy Grail War, meaning we are at the very least following the line of thought that this is a war taking 10 years after the 4th Holy Grail War, which in turn had 3 wars before that.