(1) and (5) contain plural related errors. In (1) the problem is with a noun in (5) it is with a related verb. There are also other errors in 5, but I’ll let you deal with the verb first.
2) is okay but unnaturally worded:
He wants me to join him on holiday/vacation there this year.
This year, he wants me to join him on holiday/vacation there.
3) He wants me to join him on an island vacation/holiday this year.
4) Requires ‘my’, ‘his’ or ‘her’ rather than ‘the’.