Spin dynamics of ceramic La_1-xCa_xMnO₃ with x = 0, 0.05, and 0.15 and the relative Mn⁴⁺ concentration c = 0.18-0.22 is investigated by measurements of the ac susceptibility and the relaxation of the thermoremanent magnetization (TRM). The χ_ac(T) function exhibits a transition from the paramagnetic to a mixed spin-glass and ferromagnetic phase. Below that is found a steep decrease and onset of the frequency dependence of χ_ac(T), providing evidence for existence of a reentrant spin glass (RSG) phase. The dependence of the spin-glass freezing temperature, T_f, on f satisfies the conventional critical slowing-down law, τ/τ₀=(T_f/T_G-1)^-zv with τ = 1/f, zv = 12 ± 2, τ₀→ 10^-12s and the glass temperature, T_G, decreasing from 93 to 70.5 K when x is increased from 0 to 0.15. The relaxation rate S(t) of TRM has a clear maximum near a wait time t_w→(2-4) × 10³s and the function S(T) shows a sharp maximum near T_G. The plots of S(T) exhibit a substantial decrease at T >T_G while for T <T_G they collapse into a single curve, as typical for mixed (T_G < T < T_C) and RSG phases, respectively. The observed spin dynamics agrees completely with the magnetic phase diagram (paramagnetic, mixed, and RSG phases with decreasing T) predicted recently for a system containing lattice disorder and competing superexchange and double exchange interactions.