I am surprised it is a backyard you are speaking of. This type of restriction would be a difficult one to single out statues, seems a bit discriminatory relating to your certain case. The number of items that can be placed in a back yard that are 5-6 feet are numerous E.G. Bird feeders, bird houses, water fountains, swing sets, childrens toys, umbrellas, clothes lines, ect.
In some homer owners restrictions the fence is covered under Article 8, Section 2 Part M(Fencing). It does state the "fences cannot exceed 5 Feet and shall not extend past the rear corners toward the front of the house". In my opinion this one would be tough to enforce because a lot of people including board members have fences that extend past the rear corners. However the covenant that some home owners received does not have the 5' height restriction.
Some home owners in the old and new section have been allowed to construct a 6 Ft high fence in their back and side yards. In my opnion it is discriminatory and unconstitutional to allow some residents to have 6 Ft high fences while restricting other residents to 5 Ft. high fences thus denying the person equal rights to construct a 6 Ft high fence. In my opnion once you allow one person to have a 6 Ft fence you have established a president and then everyone should be allowed to have a 6 Ft high fence