A re-entry permit allows you to remain outside the US for up to two years without abandoning your permanent resident status. These re-entry permits can be renewed once for 2 years and after that for one additional year.
The law automatically revokes your status if you are not physically present in the US for more than one year.
Since you never stayed to follow-up on your naturalization application 5 years ago, you left the US as a permanent resident. You would not become a citizen until you were sworn in at an oath ceremony.
Unfortunately since you did not protect your permanent resident status while the naturalization petition was pending you abandoned your US permanent resident status by departing and remaining outside the US for the past 3 years.
The only way to get your status back is to try to apply for a SB-1 visa which is a returning resident visa for a permanent resident who intended to return to the US and who had some intervening exceptional circumstance occur which made it impossible for them to return.
See this link which explains the requirements and procedure
If you are denied the returning resident visa then you would have to be sponsored all over again for permanent resident status, just as you were initially.
A permanent resident status is meant for you to reside in the US and if you do not reside here it is taken from you.
You may file this form to find out what happened to your naturalization application
using this form. There is no fee to request a copy of your naturalization file which would include what action was taken on it in your absence.
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