According to the site 5,000 isn't a listed threshold... there are only 2... threshold 1 is like 150 signatures and then it can become "searchable" on the site... the 2nd is 25,000... which the white house has to respond on all petitions meeting/exceeding the 2nd threshold...
I am not sure what 5,000 gets, or if that number was randomly set by the creater of the petition... I briefly skimmed it, so I may have missed alittle bit, however I did read that the whitehouse may comment on any petition regardless of threshold or signed count...