Given the dates, I can almost guarantee that you won’t find anyone you can connect to in Ancestry’s new England, Medieval Soldier Database, 1368-1374. It’s before the systematic keeping of parish registers.
Ancestry lists the contents as 15,000 records taken from The Soldier in Later Medieval England. University of Southampton: Henley Business School. That source covers the period 1369 and 1453 derived from muster rolls.
In 20 generations or so from then until now there’s a good chance one or more of those named will be your ancestor, if your English heritage goes back that far.