I'd say that's a perfectly acceptable word count. My published stories range from 3,000 to 6,000ish words. And I believe there's several in the past that have been higher; some story-driven ones I read would be above 10,000 if I had to guess.
I think it'll take a few days for the webmaster to skim through the story and make sure it doesn't break any content rules. It'll pop up in the Library and the Recent Posts page when it's approved.
Appologies for the duplicates everyone, my internet is terrible DX