I don't use the Libre so my answer is based on my CGM (Dexcom) experience. To start with, the Libre measures changes in the interstitial fluid below your skin that track actual blood glucose changes. The interstitial fluid changes generally occur about 15 minutes after the blood glucose changes.
The second thing that may be going on is the fact that this is your first day with this sensor. It's well known, at least amongst CGM users, that the first 24 hours can include erroneous readings, sometimes rather significant.
Lastly, our glucose fingerstick meters are not the most accurate or precise instruments. If your meter was off by 15%, your actual glucose could have been 85 (4.7), not 100 (5.6).
Congrats on your new D-tech. I've read so many good things about the Libre. Let us know how you're doing with it in the days ahead.