In replacing a skylight, can I reuse the existing curb and flashing

After finding water coming down my front door from inside the ceiling I had a roofer come out and take a look. He stated that the skylight was at the end of its life. This does appear to be the case as there is definite condensation between the panes and getting up on the roof I can see that all the seals do not look good.

He said it looks like the roofing is fine, and that the flashing around the skylight is fine. He recommended that I simply order a new one, pop off the old one, and screw on the new one. But I'm having second thoughts about reusing the old flashing. It appears to him to be installed correctly, and to me it looks a lot newer than the skylight (the roof was replaced 3 years ago). But will unscrewing the old one, and screwing in the new one be properly sealed?

I did go ahead and order a new one (A 4'x4' laminated VELUX), but don't want to mess things up.

EDIT: I did the work. Here's the followup.

This is before:

After:

From the inside:

1. I unscrewed the old one – noting that there were 2-3 screw holes that didn't have screws, and that there were 3 different types of screws that were used.
2. I Inspected the curb and flashing, making sure it looked sound. It did. I couldn't see any flaws.
3. I placed a little roofer's caulk in the old screw holes (not sure it was needed, but figured it couldn't hurt).
4. I placed the new skylight over the existing curb and flashing.
5. I screwed in the new skylight using the screws that came with it – pressing down on the frame while doing so.

Time will tell but I think it works.