IMO that heart rate sounds "about right". I test VO2max and other performance variables in a lab on people of all fitness levels, and just as ballpark numbers go that is on the low end of cardiorespiratory fitness, but isn't anything to toss out a perfectly good heart rate monitor over.
Individual variability in such things as economy of movement, in conditioning level, proportion of lean mass, etc, taken into account, it makes sense that even a slow pace like 5.1 mph could elicit such a high heart rate.
Toonces said it right, your heart rate will lower for the same pace as your conditioning level improves! I'll also agree with the use of the 60% HRmax guideline for staying in your aerobic zone, though it may just be that any speed of running may put you outside of that zone until you get more fit.
I question your need to stay in the "fat-burning zone". While in this zone, your metabolism is truly selecting fat as the primary source (fat only burns with oxygen). However, higher intensities burn more total calories, including the maximal rate of fat it can handle. By demanding more force production, higher intensities also promote muscle growth, which itself increases metabolic rate and thus burns more daily calories.
I say run! Humans were evolved to run. I am quite sure that after 4-6 weeks you will notice a significantly lower heart rate at those speeds. After that, begin adding intervals of 60-90 seconds of 6-8mph and you will zoom to the next level of fitness very quickly.
Good luck! Running changes lives.
