Your probelm is you only have 5-acres to hunt. With only 5-acres you will need to shoot them in the head with a rifle. This is the only way I know to make sure they die on your land.
I forgot to mention I like the idea of a chain link fence. You can leave holes in it were you want the deer to enter your property. The chain link fence can be erected in a fraction of the time it would take to constuct a "eco-fence". The eco-fence also becomes a fire hazard & makes it look like sanford & son own the property.
IMHO this is not unethical or against any fair chase rules.