Using 'date' in bash shell to add 5 minutes to a defined time with high precision

Seemingly in conflict with other use I've been able to find of date -d It turns out the way to add minutes that works for me is:

TIME="23:01:05.001"
echo $TIME
date -d "$TIME 5min" +"%H:%M:%S.%3N"

23:01:05.001
23:06:05.001