Four of the incidents were in the Skegness area and one in Louth - with two women in their 60s and two women and a man in their 70s among those receiving telephone calls from scammers claiming to be from police stations across the county. Other incidents have been reported in the Boston and South Holland areas.
The police say impersonators claiming to be detectives are using various names such as Mark Warren, Mason Greenwood and Andy Graham.
PCSO Dave Bunker of Skegness warns the callers are very convincing.
"We hear a lot that callers claim to be from the police investigating a crime involving a family member and a cloned bank card," he said.
"They ask for bank details, which the police would never do, and tell the victim to call them back on 161.
"It is at this point they do not hang up and when the victim calls 161, they are still on the line but another voice answers saying 'police' and identifies the 'officer' dealing with the case before 'putting them through' - or in reality just hands the phone back to the original caller."
Inspector Jacky Barnsley for the coast said: “Luckily, none of the victims handed over any money. We would like to thank the public for their assistance so far in informing their elderly and vulnerable neighbours but we would ask if you can please keep visiting them to reinforce the message that a police officer or bank will never ever ask for you to hand over any money or for your bank details.
"Please never give out any details to anyone who calls asking for them.”
Detective inspector Kara Nicholson has asked for residents warn vulnerable neighbours. She said: “Please take a few minutes out of your day to visit your vulnerable and elderly neighbours and tell them about these scams.
“We are becoming increasingly concerned as these scammers are targeting the elderly and vulnerable. We need to make them aware that the police, their bank or any other legitimate organisation would never ask them for money.
“If anyone calls and asks for money please hang up the phone and call us on another line. If you do not have another line then please ask a neighbour to call us.
“Scammers can be very clever and sometimes use a phone number that replicates your bank’s telephone number. They also make out they are police officers. Do not be fooled and please hang up on them.”
If you receive a call and are unsure, please hang up the phone immediately and call 101 on a different line. Always call 999 in an emergency.
You can also report the call to Action Fraud on 0300 1232040.
Operation Signature works alongside other organisations, such as Lincolnshire Trading Standards, to raise awareness of this and many other types of fraud.
Follow Op Signature at its dedicated Twitter account: @Op_Signature
For more information on fraud visit: https://www.lincs.police.uk/news-campaigns/news/2019/police-impersonation-fraud/Operation Signature works alongside other organisations, such as Lincolnshire Trading Standards, to raise awareness of this and many other types of fraud.