Hi

Normally the rule says that you must move two consecutive coins

To find the solution start from the end

OOOoo

The last movement involved one blue coin and one red coin that must be consecutive : there is only one choice (the third and fourth coins)

OO__oOo : this leads to a dead end

OoOO__o : this one works. Find the last but one movement and so on

The job can be done in 5 movements