I Used Also Find My App But No Benefits
Find My has to be enabled on the phone.....before.....it is lost. You did not indicate whether that was the case.
Even if Find My has been enabled, the phone will not show up on the Find My map if.....
- The battery has run down
- The phone has been powered off
- The phone does not have an Internet connection where it is currently located
The IMEI won't help. Your carrier will not try to locate the phone unless this is a case of missing person. Even then, the carrier will require a court order to act.
If you really did lose the phone 4-5 months ago, I'm sorry but you have to be realistic about things. You will never find the phone.
Phones that are "found" are those that are located within a day or two of being lost. Even after a week or two, there's virtually no chance of finding the phone.