You can use the integer division and multiply back to get the round value.
$ m=23
$ (( m /= 5, m *= 5 )) && echo $m
20
Integer division just return the integer part of the result, so in the case above is returning 4. Then multiplying by 5 gives 20.
In your case:
$ TIMESTAMP=$(date "+%Y%m%d%H%M")
$ echo $TIMESTAMP
201404011231
$ (( TIMESTAMP /= 5, TIMESTAMP *= 5 ))
$ echo $TIMESTAMP
201404011230
$ TIMESTAMP=$(date "+%Y%m%d%H%M")
$ echo $TIMESTAMP
201404011257
$ (( TIMESTAMP /= 5, TIMESTAMP *= 5 ))
$ echo $TIMESTAMP
201404011255