4 or 5 Time Constants to reach practical potential?
The correct answer to this question would have to be: Neither, the set point is insufficiently specified.

To elaborate: 


Let us say the component in question is a capacitor, to be charged / discharged. 
As this charging / discharging process approaches limit asymptotically, clearly there is no finite time to completion, as the question rightly notes.
Thus, to specify sufficient condition for "reaching practical potential", an acceptable variance from the asymptotic value must be specified.
This may typically be specified as a percentage, say "within 1% of supply voltage"
Depending on the percentage specified, the number of time constants to fulfillment would be calculated, as the question already mentions. 


Thus, both textbooks are correct, with the caveat that neither mentions acceptable percentage (or the question has not reported this).