Since the doc hasn't replied to this question (yet), your Vit D levels are low enough to warrant supplementation. In my country it is common to supplement with

Since the doc hasn't replied to this question (yet), your Vit D levels are low enough to warrant supplementation. In my country it is common to supplement with 60K IU once a week, for 8 weeks, before moving to a maintenance dosage of 60k once a month. That's almost 10k IU/day during the loading phase. You're at 5k IU/ day, so should be fine. In comparison, a fair skinned person at the beach on a sunny day will make over 10k IU of D3.