Secular period variations, {beta}=dP/dt, in 76 RR Lyrae stars in the globular cluster M5 are analysed using our most recent CCD V photometry and the historical photometric data base available in the literature since 1889. This provides a time baseline of up to 118 yr for these variables. The analysis was performed using two independent approaches: first, the classical O-C behaviour of the time of maximum light, and second, via a grid (P, {beta}), where the solution producing the minimum scatter in the phased light curve is chosen. The results of the two methods agree satisfactorily. This allowed a new interpretation of the nature of the period changes in many RR Lyrae stars in M5. It is found that in 96 per cent of the stars studied no irregular or stochastic variations need to be claimed, but that 66 per cent of the population shows steady period increases or decreases, and that 34 per cent of the periods seem to have been stable over the last century. The lack of systematic positive or negative period variations in RR Lyrae stars in other globular clusters is addressed, and the paradigm of period changes being a consequence of stellar evolution is discussed in terms of chemical variations near the stellar core and of multiple stellar populations. In M5 we found a small positive average value of {beta} and a small surplus of RRab stars with a period increase. Nevertheless, in M5 we have been able to isolate a group of likely evolved stars that systematically show positive, and in some cases large, period change rates.