In UK IF Dan was 5 in June ....it would be almost the end of the school year .. UK school year starts in September and finishes July. Summer holidays are middle ish July to end of August / early Sept. SO Dan would start school at the beginning of the new September term. BUT in some places he could start at the beginning of the Term after Easter.... April / May time ! Not quite 5 but close !
As it happened Dan was 5 in UK.... Oct. 2nd and he started school in the new September year before he was actualleh 5... well 4 weeks before he was 5 !
In NZ they can start when they are 5.. on their 5th birthday unless it is school holidays like Jack and Cash ! In NZ Annie 13th Jan. (Still Christmas / summer holiday) started when she was 5 years and 2 weeks

Matt, May 7th started after the Easter holidays and he was not quite 5 .. but almost.