No, normally you cannot reinstate your same insurance policy after 5 months of having a lapse. You can easily quote and purchase a new policy through CarInsurance.com to obtain a car insurance policy.
Reinstatements are allowed by most companies but only up to 30 days. Car insurance providers that will reinstate within 30 will require you sign a statement of no loss. This is a form stating you have not had a loss in the time you had the lapse and that you could and would not make a claim for that time period. Some companies may charge you a reinstatement fee to reinstate your policy.
So while most carriers will usually reinstate a policy that has cancelled due to non-payment, as long as the lapse in coverage has been less than 30 days and there have been no losses, they will not reinstate a policy that has been cancelled for five months.
Some insurance companies have a grace period of 7 - 10 days in which you have to reinstate your policy (if you had not had any losses of course). If you reinstate within "grace period" of the cancellation date you can get the same rate but you must pay a certain amount of months upfront, 2 to 6 typically. After that grace period they may still reinstate you up to 30 days but there are additional fees which you must pay upfront along with certain amount of months paid in full upfront. After 30 days generally you will have to sign up again with the insurance company or since you are getting a new policy shop around for insurance with another carrier.
Insurance companies' guidelines and state laws do differ however so you can contact your agent about your lapsed policy to see if there is a way to reinstate it or if you will need to start up a new policy. You can start shopping for a new auto insurance policy here with us even if you have had a 5 month lapse in coverage.