Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
GET GOLEM BUFF!!!
Cleanse/Heal: Since Gangplank has his own built in Cleanse + Heal, do not take these.
Teleport: Can be useful, especially if laning mid. This shouldn't happen, unless it's a very unorthodox team.
Exhaust: It takes a while to build Frozen Mallet. Exhaust is extremely useful for getting kills/escaping before this stage.
Flash: Still a very powerful skill. Has so many uses, including escaping through walls, getting one last Parrrley in, avoiding skill-shots, etc.
Ignite: Part of Gangplank's passive is a MS effect, so this part of Ignite is wasted. Still useful for getting kills.
Ghost: I use it during team fights to stay out of the way, but still be able to Parrrley into whoever I want. Pro-tip: you can ghost through Anivia's Crystallize.
Smite: Useful for early gold, and to make up for Gangplank's early game being limited versus ranged opponents.
Avarice Blade: Depends on how well you do at the start, but I mostly ignore them. If you plan on ganking (not being in the lanes as much), they might be a reasonable investment. Don't buy any past the 15-minute mark.
Frozen Mallet: If you get this early you gimp your Parrrley damage, but the slow can possibly net you the same amount of success. Remember that your Parrrley will apply the slow too. Ymmv.
Chalice of Harmony: I find it's difficult to do well without it. If you stack mana regen glyphs it's decent after mid-game. Without Chalice I tend to harass and deny less.
I know that the passives of Infinity Edges don't stack, but it's still the best item for gangplank as a 6th item (sell Chalice).
P.S. If you're going to vote on this build, please leave a comment to say why you did and offer suggestions if you have them.