Just to add a point..
Apple repeaters (extend wireless) all have to connect back to the main AEBS.. you cannot extend and extender.
And 5 AEBS that connect wirelessly is far too many.. They will interfere with each other.
I would say one base and two extenders.. at most.
Even in the scenario Tesserax has quoted of connection with ethernet.. they still should be far enough away from each other to have no overlap. With only 3 non-overlapping channels in 2.4ghz.. 1, 6, 11 that means you need at most 3 in any one area.. of say 20-30 feet in a normal house. Normally, unless you live in a barn or a sultan's palace 3 should be enough.