Graph Algorithms · Hard problem

Six warehouses $1$–$6$ can be linked by cables with costs (in thousands of dollars) $12{:}5$, $13{:}9$, $14{:}3$, $23{:}4$, $25{:}8$, $34{:}6$, $35{:}7$, $46{:}2$, $56{:}10$. Instead of the CHEAPEST way to connect all six warehouses, a rival planner wants the costliest possible set of $5$ cables that still connects all six warehouses without wasting a cable on a cycle (a maximum spanning tree). What is that greatest possible total cost?