A few things:

1. You started at 5 am: early morning runs can be very very sluggish even for people who are good at running.
2. 10 miles a week, while respectable, is simply not a lot. Just keep increasing, slowly, the weakly volume.
3. There's an overemphasis lately on the easy runs. Sometimes you should get tired. Sometimes very tired. Maybe once every 2 weeks, since you're only running 3x a week. Consider some fartleks.

Edit: some additions:

4. Almost against the previous point but not really: while you should get very tired sometimes, easy runs have to feel easy/comfortable. Forget what your watch is telling you about heart rates and zones and all that. Listen to your body.

5.Your legs getting tired could be a number of things: lactate build up (going too fast),not enough recovery from harder runs/leg strength workouts, muscle fatigue from being unconditioned to longer runs (solution is also to just keep running more and easy).

6. Have patiente. Don't force a pace that is not there yet, let it come naturally as a consequence of sustainable long term training.

You can and probably should continue to slowly try to increase the total amount of easy km, like many have said, but I also believe you should incorporate some specific sessions to increase speed and strength. Just "run more" will only get you so far. These sessions should be a small percentage of the total amount of kms you're running weakly, but if you do them consistently you'll see results. These sessions can be fartleks and hill sprints. A sugestion for a fartlek you could be doing is 30s-60s fast, 60s very slow but not walking for 15-30 minutes total. Don't worry if you don't know how fast you should go yet, just go and do it and don't be afraid to get tired. In fact, please get tired, these are supposed to be hard workouts. You'll learn the paces with experience and by paying attention to your body.

Another thing: don't compare yourself to others or to what times the internet tells you are the averages. Also, you really can't compare... not even to yourself. You haven't raced yet. Training sessions can give you some insight, if you have enough experience, but they can never be a true test of your abilities, only a race can. You simply don't know what time you can do for 5km. "Don't race your training"

And a final thought, these sort of plans, couch to something, are good to get you moving. You've got that and that is fantastic and beautiful. Don't diminish that accomplishment. But now, at the end of the plan, it's time you begin to learn that you can suffer a lot more than what you think you can.