I found a 5 by picking two Random article pages:

Xyloplax turnerae to Pagolo Arsago -- https://www.sixdegreesofwikipedia.com/?source=Xyloplax%20tur...

I love all the little touches, like the fun facts (2.51% of Wikipedia articles don't have incoming links) and UI touches ("wipes brow, I really had to work hard for this one").

I noticed that pages about countries are good hubs for this kind of connection. The page cites someone, their page has a link to his country of origin and these country pages are really extensive and have links to a variety of topics.

Edit: I finally managed to find a 5 degree route! https://www.sixdegreesofwikipedia.com/?source=Taquaral&targe...

I got 9 steps with "Here (company)" to "There (wikipedia disambiguation page)".

I got a 9 step one without a disambiguation page. https://www.sixdegreesofwikipedia.com/?source=Lion%20Express... Took a long time though.

Disambiguation pages are not supposed to be linked from within Wikipedia, so I'm not sure this one really counts.

Got five! https://www.sixdegreesofwikipedia.com/?source=Living%20Compu...