See the history of the Cinque Port Arms on the website below:
http://www.dover-kent.com/Cinque-Ports-Arms.html
This is part of a comprehensive history of all the pubs in Dover originally compiled by Barry Smith in his work "By the Way" and constantly updated by Paul Skelton to give the definitive website version below which constitutes a fascinating social history of Dover:
http://www.dover-kent.com/1Pubs-list.html
Incidentally, the pronunciation of Cinque Ports is indeed "sink ports" as per the phonetic spelling in Brian's post, and not "sank ports" as one might expect, since it is derived from old French. Click on the little loudspeaker symbol on the link below. To be pedantic, the pub name is actually Cinque Port Arms not Cinque Ports Arms.
http://oald8.oxfordlearnersdictionaries.com/dictionary/the-cinque-ports