I’m assuming by local space you mean the noob’s local space. In this case you can easily do:
local origin = workspace.Noob:GetPrimaryPartCFrame()
workspace.Noob:SetPrimaryPartCFrame(origin * CFrame.new(0,5,0))
Basically multiplying CFrame matrices is like “applying a local offset to another local offset”, so in this case we’re applying 5 stud offset on the y in the origin’s local space.
I also want to mention that SetPrimaryPartCFrame starts shifting its children around when called multiple times, so I would advise against using this function in a loop or something.