The members of the Rail, Maritime and Transport union will down tools over two weekends from Friday 12 August to Monday 15th August and then for three days over the British bank holiday weekend from August 27th.
The union said the action was being taken due to Eurostar's failure to honour an agreement from 2008 that sought to ensure train managers could expect a good work-life balance in terms of unsocial hours and duty rosters.
Members say their work-life balance is being repeatedly undermined.
The RMT general secretary Mick Cash said: “Our members have every right to have a fair work-life balance that fulfils operational needs of the company while guaranteeing quality time off for friends and family.
“It's now time for Eurostar to come to the negotiating table with a set of proposals that honours our agreements and guarantees our members a genuine work-life balance.”
Around 80 train managers are involved in the dispute but Eurostar suggested the strike would have little impact on services saying it would make some "small changes" to the timetable as a result.
A spokesman for the company said: "We are aware of the plans for strike action and our focus has been seeking a joint resolution whilst planning to provide a good service for our customers.
"On the days of the strike we have made some small changes to our timetable to ensure that all passengers booked to travel will be able to on those days. Passengers affected will be notified in advance."