The theoretical and experimental values of the 5f, 6f, 7f, and 8f radiative lifetimes of neutral potassium are reported. The reduced matrix elements for all allowed electric-dipole nf 5/2 -nЈd 5/2 , nf 5/2 -nЈd 3/2 , and nf 7/2 -nЈd 5/2 transitions with n =5-8 in K are calculated using the relativistic linearized coupled-cluster method with single and double excitations of Dirac-Fock wave functions included to all orders in many-body perturbation theory. The resulting electric-dipole matrix elements are used to evaluate the lifetimes of the 5f, 6f, 7f, and 8f states in neutral K and their uncertainties. The contributions from the nf 5/2 -nЈg 7/2 , nf 7/2 -nЈg 7/2 , and nf 7/2 -nЈg 9/2 transitions to the lifetimes of the 6f, 7f, and 8f states are evaluated using the third-order manybody perturbation theory and are found to be very small. The theoretical results are 5f = 117͑4͒ ns, 6f = 195͑4͒ ns, 7f = 301͑6͒ ns, and 8f = 441͑9͒ ns. The experiment is performed in a cell using time-resolved fluorescence spectroscopy. The nf states are excited stepwise, 4s → 4p → nf, using two pulsed synchronous dye lasers for the dipole and quadrupole transitions, respectively. The measured values 5f = 117͑3͒ ns, 6f = 190͑6͒ ns, 7f = 309͑8͒ ns, and 8f = 428͑10͒ ns are in excellent agreement with the present theoretical calculations.