Ask the mechanic if he’s going to pay for the change at 5K. Your free maintenance covers the change at 10K not at 5K. Further, a change at 10K intervals is more than adequate. I’ve got an 09 TDI Jetta with the same engine as your 2010. I had an oil sample analyzed by Blackstone Laboratories after 5K. The analysis indicated that the oil was good for many more miles. I had it changed after 10K miles. I had it analyzed again by the lab just before the 20K service. The oil at that time had almost half of the original additive package, and the metals in suspension were minimal, so it could have gone even further than 10K miles.
In summary, assuming you use the proper 507 VW specification oil, the oil is easily good for 10K miles. Just go by what your Owner’s Manual recommends. (10K changes)