Some Ideas for Your Further Investigation
Others will know more, but would doubt that the presumably stock zincs on a recently designed/manufactured boat are so undersized that they need to be replaced every 5 weeks. You could double the zincs and still be replacing in a much too short a time frame. Likely something else is going on.
1) The following might be helpful for an overview of galvanic corrosion and the role of zincs: http://www.boatus.com/boattech/casey/23.htm
2) Your marina is electrically "hot". Use the archive feature of this forum and type in "hot marina" and click on the exact phrase option to find threads for description, diagnosis tips and solution ideas.
3) Being connected to shore power 24/7 I've read ususally will cause the zincs to go faster, lot more so if the marina is also hot. I have a solar panel to keep the batteries topped up and generally only connect to the shore grid when I'm on board working with power tools or want to watch the TV. Just last week a diver was bottom cleaning and replacing zincs on my neighbor's boat and I asked him to take a look at my 10 month "in the water" zincs. The shaft zinc he said had almost no depletion and the prop zinc was still 85% good. The neighbor connected to shore power needs to have his zincs replaced every six months or so.
Lots of variables and people probably have written discertions on the subject. I used to work for a an ocean transportation company operating large bulk carriers (lots and lots of steel needed protection). Sacrificial Anodes (zincs) featured high up in the replacement parts/maintenance budget.