To avoid confusion, it is advisable to state what exactly "The following" refers to.
Also, will Ann be checking these items? If so, the items are "to be checked by Ann".
(1) The following items (plural noun) have (plural verb) to be checked [by] Ann:
Sometimes, we omit what comes after "following" since a list is also provided:
(2) The following have (plural verb - since there are several items) to be checked [by] Ann:
If you consider the five items as a list, then you can write:
(3) The following list of items has (singular verb - since there is A list) to be checked [by] Ann:
Are you asking someone to check the items WITH Ann?
If so, you can write: You have to check the following (items) with Ann: / You have to check the following list (of items) with Ann:
I hope this helps.