We present an analysis of the Qatar-1 and TrES-5 transiting exoplanetary systems, which contain Jupiter-like planets on short-period orbits around K-dwarf stars. Our data comprise a total of 20 transit light curves obtained using five medium-class telescopes, operated using the defocussing technique. The average precision we reach in all our data is $RMS_{Q} = 1.1$ mmag for Qatar-1 ($V = 12.8$) and $RMS_{T} = 1.0$ mmag for TrES-5 ($V = 13.7$). We use these data to refine the orbital ephemeris, photometric parameters, and measured physical properties of the two systems. One transit event for each object was observed simultaneously in three passbands ($gri$) using the BUSCA imager. The QES survey light curve of Qatar-1 has a clear sinusoidal variation on a period of $P_{star} = 23.697 pm 0.123$,d, implying significant starspot activity. We searched for starspot crossing events in our light curves, but did not find clear evidence in any of the new datasets. The planet in the Qatar-1 system did not transit the active latitudes on the surfaces of its host star. Under the assumption that $P_{star}$ corresponds to the rotation period of Qatar-1,A, the rotational velocity of this star is very close to the $v sin i_star$ value found from observations of the Rossiter-McLaughlin effect. The low projected orbital obliquity found in this system thus implies a low absolute orbital obliquity, which is also a necessary condition for the transit chord of the planet to avoid active latitudes on the stellar surface.
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