We present our monitoring campaign of the outburst of the black-hole candidate Swift J1753.5-0127, observed with the Rossi X-ray Timing Explorer and the Swift satellites. After ~4.5 years since its discovery, the source had a transition to the hard intermediate state. We performed spectral and timing studies of the transition showing that, unlike the majority of the transient black holes, the system did not go to the soft states but it returned to the hard state after a few months. During this transition Swift J1753.5-0127 features properties which are similar to those displayed by the black hole Cygnus X-1. We compared Swift J1753.5-0127 to one dynamically confirmed black hole and two neutron stars showing that its power spectra are in agreement with the binary hosting a black hole. We also suggest that the prolonged period at low flux that followed the initial flare is reminiscent of that observed in other X-ray binaries, as well as in cataclysmic variables.