CrossRoads seems to be assuming you do have them in series.
There is no particular reason a star topology precludes you from chaining them, it simply means the shift out from each has to return through the hub wiring and pass out to the next input. Since there is only one load on it, it is somewhat less of a problem than the loading on the driver for the five radials of clock and latch.
If however you must access each separately, it is the latch line that is distributed separately to each. Clock and data will load each shift register with the same data, but only the one whose latch is strobed, will exhibit that data (though you could of course in this fashion, exhibit the same data to any number of latches simultaneously).
Using a 74HC14 for each of the data and clock, you can buffer five lines with one inverter feeding the other five, a separate output line for each.