Using two different spectrographs, High Accuracy Radial velocity Planet Search (HARPS) (European Southern Observatory) and SOPHIE (Observatoire de Haute Provence), we have measured vsini for a sample of dK5 stars. These are the first measurements of vsini for most of the stars studied here. We measured vsini to an accuracy of 0.3km/s and a detection limit of about 0.5-1km/s. All our targets have similar (R-I)c colour. This is an advantage and facilitates the determination of the narrowest line profiles for vsini~0. In our total sample, we detected rotation for 22 stars (three dK5e and 19 dK5 stars), and we did not detect rotation in a further 22 stars. This result shows that there are many dK5 slow rotators, and many more than for dM1 stars. We also report on a newly discovered dK5e star, McC 522, which is also the fastest rotator in our sample.