Jamaica Plain businesses would get five new booze licenses a year for three years under a proposal floated Monday. Mayor Marty Walsh and City Councilor At-Large Ayanna Pressley announced the plan, which would add a total of 105 licenses to JP, Hyde Park, Roxbury, East Boston, Dorchester, Mattapan and Mission Hill. In a holdover from the days when the state did not trust Boston to distribute its own booze licenses, a restauranteur faces six-digit costs and Byzantine rules to serve vodka, stout or chardonnay. All licenses are tightly regulated and involve approvals at both the state and city levels. Pressley, taking up liquor licenses as an economic development issue, shepherded a similar program through in 2014.