The Short Version
Most adults are unlikely to develop side effects from 5,000 IU of vitamin D daily, and several studies found it was generally well tolerated. But the claim overstates the evidence: 5,000 IU is above the usual adult upper limit of 4,000 IU, and review-level evidence shows a small but real increase in some adverse events at nearby doses. A safer wording would be that side effects are uncommon, not absent.