B[e] stars are surrounded by cool and dense circumstellar environments where molecules and dust are formed. These stars are rare and display complex spectra whose photospheric features are frequently veiled by their circumstellar envelopes, making it difficult to assign them spectral types and evolutionary phases. On the basis of a detailed analysis of medium-resolution spectra in the near-infrared region, together with optical observations and available data from astronomical databases, we attempt to improve their spectral classification and infer the properties of their circumstellar environments. To this aim, we have selected a group of five bright IRAS sources (IRAS 02155+6410, MWC 728, AS 119, MWC 819, and IRAS 07080+0605): one star with large infrared excess and four unclassified B[e] stars or FS CMa stars, most of which have been poorly studied. We present and describe our observations and discuss possible classifications of the sample objects. For all stars, medium-resolution spectra in the region of 2.17-2.39 μm and in the L band are shown for the first time. Infrared features, such as the absorption molecular CO bands and metallic lines, reveal the presence of a late-type companion in MWC728, and suggest the possible binary nature in AS119. IRAS07080+0605 shows evidence of a surrounding cool CO molecular cloud. CS molecular emission may be present in MWC 819 L-band spectra. We suggest that this object is a protoplanetary nebulae.