Results are presented of a search for heavy stable charged particles produced in proton-proton collisions at sqrt(s) = 13 TeV using a data sample corresponding to an integrated luminosity of 2.5 inverse femtobarns collected in 2015 with the CMS detector at the CERN LHC. The search is conducted using signatures of anomalously high energy deposits in the silicon tracker and long time of flight measurements by the muon system. The data are consistent with the expected background, and upper limits are set on the cross sections for production of long-lived gluinos, top squarks, tau sleptons, and leptonlike long-lived fermions. These upper limits are equivalently expressed as lower limits on the masses of new states; the limits for gluinos, ranging up to 1610 GeV, are the most stringent to date. Limits on the cross sections for direct pair production of long-lived tau sleptons are also determined.