The dielectric permittivity and loss spectra of the glassy state of 5-methyl-2-hexanol obtained by quenching it from the liquid state has been studied. In one experiment, the spectra were studied at different temperatures as the quenched sample was heated at 0.1 K/min from 105.3 to 160.5 K. In the second experiment, the quenched sample was heated from 77 to 131.6 K and kept at that temperature for 14.6 ks. The relaxation rate, f(m,beta), the dielectric relaxation strength, Deltaepsilon(beta), and the distribution of relaxation time parameters, alpha and beta, for the Johari-Goldstein process were determined. The parameter beta was found to be equal to 1 and independent of both the temperature and time, Deltaepsilon(beta) initially decreased on increasing the temperature, reached a minimum value at similar to145.6 K, and then increased. The plot of f(m,beta) against the reciprocal temperature decreased in slope and at similar to140 K became linear. This indicates that f(m,beta) increases on structural relaxation. In the course of the annealing at 131.6 K, Deltaepsilon(beta) of the quenched sample decreased with time, approaching a plateau value. It is described by an equation, Deltaepsilon(beta)(t)=Deltaepsilon(beta)(t-->infinity)+[Deltaepsilon(beta)(t=0)-Deltaepsilon(beta)(t-->infinity)]exp[-(t/tau)], where t is the time, and tau (=3.5 ks) is the characteristic time. It is pointed out that contrary to the earlier finding, o-terphenyl shows a beta relaxation in the equilibrium liquid state. A consideration of dielectric permittivity arising from small-angle motions of all molecules, which has been suggested as an alternative mechanism for the localized motions seen as beta relaxation, indicates that this mechanism is inconsistent with the known increase in the equilibrium permittivity on cooling.