I have 3 dui's in my record. can I own a hand gun in south dakota

I would call your sheriff's department and ask them

yes you can as 5 years have passed and you not committed any other felonies

In the District of Columbia and every state (except perhaps one), either federal or state law explicitly or implicitly bars gun possession by persons with multiple DUIs.[3]

I would doubt it since one requirement is you are not habitually intoxicated or in a drugged condition. With 3 dui's on your record you would be challenged on this issue.