I have a GOMOR in my OMPF from a DUI. Can I get it removed through DASEB?

Ssg James Preston I too admire your resilience and pushing on even with the constant doubt from others. I will tell you can have that Gomar moved to your "Restricted File". As someone who has been through the DASEB to get "unfavorable Information" removed and talking from experience. Clearly you meet the time requirements since it's been 5 years ago. Also you have to show that the punishment served its purpose and you have grown since that Gomar. I was always made to believe that the Army forgives if you do x.y.z and so forth but it never felt good Validating year after year for the board and seeing that blackmark against me. It definately hurt me for alot of years and it was a red flag evey year I was being considered. Long story short go through the DASEB and submit your packet. It's your only shot if you want to progress and it's a long process. Once my "unfavorable Information" was moved over. I picked up the next year and been grinding since then. Good luck and keep on striving!

I am not a military lawyer, and you need one.
That said, reading of chap 7 in AR 600-37 a laymen's reading indicates to me, you do not have a valid appeal.
As the SM filing the appeal.. you must
"(b) The recipient has the burden of proof to show, by clear and convincing evidence, to support assertion that the document is either untrue or unjust, in whole or in part."
Is it untrue you got a DUI?
Is it unjust you got a letter of reprimand for getting a DUI?
I think the answer to both qualifying questions is no.

Also very telling are two other points...
In this same chapter, it states even the officer that gave you the reprimand can not have it rescinded because "it has served its purpose"
And 2nd, discharge upgrades....they can not be approved because of what has happened AFTER. TO get a discharge upgraded you must prove it was wrongly issued.
It seems clear the Army's intent is not to rescind, upgrade, ect based on good behavior after the fact.
Bottom line, these boards are made up of humans, they can act humanish sometimes and follow what they feel is "just" or "right" vice an interpretation of the reg that says they must say no.
So get some real educated with mil law and regulations experiences to assist in writing your appeal.
If you dont try, you for sure wont get it rescinded.

To give you some light about possibly overcoming the GOMOR...I knew a 1LT that had received one when he was a SSG (or SGT...he never specified what rank he was when he got it) but he made SFC and then get a commission. And this was after everyone told him he would never make SFC nor get the commission.