The fifth-order nonlinear response is analyzed applying incoherent broadband laser light with femtosecond autocorrelation time under nonresonant conditions. Raman-like excitation is performed combining the broadband incoherent laser with a quasi-cw narrow-band laser with a frequency difference of both lasers tuned to match the frequency of a nuclear mode. The pulsed broadband laser is split into three identical beams allowing application of two different time delays between them. Similar to experiments with single fs pulses, Raman double excitation allows to discern homogeneous and inhomogeneous broadening of the nuclear response. The separation of the broadening contributions, however, demands careful analysis of the signal dependence on delay time in the tail of the observed peaks. Particular features of the experiment, which is described in the second part of this paper, as interferences with cascading of third-order processes and a deconvolution procedure to extract the molecular parameter from the experimental data are theoretically discussed.