Hi Cody,
Apologies for the late reply, I was working at a conference last week.
> Can the enterprise geodatabase(oracle) release( in our case 10.5.1) be higher than the ArcGIS Server release( in our case 10.4.1)?
If you mean to use the enterprise geodatabase as a valid data source to power web services - I think this should be ok. Although any new functionality available in the higher release geodatabase would NOT be accessible within the web service. I'm not even sure if there were any major functional changes.
While I have not personally tested this configuration, I am not aware of any issues that would arise from this deployment. Although the best and recommended option would be to have both your enterprise geodatabase and ArcGIS Server site at the same release.
Hope this helps,