Two separate groups of men travelled hundreds of miles from England to Anglesey before being stopped by police.
Officers from North Wales Police first stopped a group of three men driving in a vehicle near the Menai Bridge on Friday (May 22).
The men, who all live at separate addresses, had made the 112-mile journey to the island from Manchester - despite lockdown restrictions being in place.
They had been heading to Llangaffo but were told to return home and were reported for breaching Covid-19 rules.
Later that day, officers sent a further two men back to England after they travelled more than 125 miles from Stoke-on-Trent to Newborough Beach.
North Wales Police Anglesey wrote on Facebook: "Officers have been on patrol across the island.
"A car was stopped on the approach to the Menai Suspension Bridge.
"In the car were three males who had driven from Manchester...
"All three were from different addresses so were ordered to return home and all three have been reported for breaching Covid-19 offences.
"Two men were also sent back home after being found on Newborough beach after travelling there from the Stoke-on-Trent area. Both have also been reported.
"Patrols will continue throughout the bank holiday weekend.
"Restrictions remain here and visitors will be welcomed back once it is safe and right to do so."
Watch: On patrol with the police trying to stop people coming from England into Wales
The top fine for people caught repeatedly flouting lockdown rules in Wales has been increased.
The existing system, which has a maximum fine of £120, will be replaced by a structure where the penalty doubles with each offence up to a maximum of £1,920 for the sixth breach.
On Monday, Mr Drakeford told BBC Radio Wales Breakfast that examples of people travelling from England to Wales are "concerning".
People in England are allowed to drive to another location to exercise, but people in Wales are not due to differing lockdown restrictions.
