date --date="5 min ago"
you may need to play around with the output format
man date
for details
then you could just grep that date, with a silly 'after' ( -A 5000 )
Code:
FiveMinAgo="$(date +"%b %d %H:%M" --date="5 min ago")
SixMinAgo="$(date +"%b %d %H:%M" --date="6 min ago")
grep -A 5000 "${FiveMinAgo}" /path/to/log.log || grep -A 5000 "${SixMinAgo}" /path/to/log.log
don't know how often that log is written to
You may need to be 'smarter'
but you have something to work with ( don't expect the above to be fool proof, it isn't )