Selecting sources with rising flux densities towards longer wavelengths from Herschel/Spectral and Photometric Imaging Receiver (SPIRE) maps is an efficient way to produce a catalogue rich in high-redshift (z > 4) dusty star-forming galaxies. The effectiveness of this approach has already been confirmed by spectroscopic follow-up observations, but the previously available catalogues made this way are limited by small survey areas. Here we apply a map-based search method to 274 deg2 of the Herschel Multi-tiered Extragalactic Survey (HerMES) Large Mode Survey and create a catalogue of 477 objects with SPIRE flux densities S500 > S350 > S250 and a 5σ cut-off S500 > 52 mJy. From this catalogue we determine that the total number of these `red' sources is at least an order of magnitude higher than predicted by galaxy evolution models. These results are in agreement with previous findings in smaller HerMES fields; however, due to our significantly larger sample size we are also able to investigate the shape of the red source counts for the first time. We have obtained spectroscopic redshift measurements for two of our sources using the Atacama Large Millimeter/submillimeter Array. The redshifts z = 5.1 and 3.8 confirm that with our selection method we can indeed find high-redshift dusty star-forming galaxies.