A framework is outlined to assess Cepheids as potential cluster members from readily available photometric observations .
A relationship is derived to estimate colour excess and distance for individual Cepheids through a calibration involving recently published HST parallaxes and a cleaned sample of established cluster Cepheids .
Photometric V–J colour is found to be a viable parameter for approximating a Cepheid ’ s reddening .
The non-universal nature of the slope of the Cepheid PL relation for BV photometry is confirmed .
By comparison , the slopes of the VJ and VI relations seem relatively unaffected by metallicity .
A new Galactic Cepheid confirmed here , GSC 03729-01127 ( F6-G1 Ib ) , is sufficiently coincident with the coronal regions of Tombaugh 5 to warrant follow-up radial velocity measures to assess membership .
CCD photometry and O–C diagrams are presented for GSC 03729-01127 and the suspected cluster Cepheids AB Cam and BD Cas .
Fourier analysis of the photometry for BD Cas and recent estimates of its metallicity constrain it to be a Population I overtone pulsator rather than a Type II s-Cepheid .
AB Cam and BD Cas are not physically associated with the spatially-adjacent open clusters Tombaugh 5 and King 13 , respectively , the latter being much older ( \log \tau \simeq 9 ) than believed previously .
Rates of period change are determined for the three Cepheids from archival and published data .
GSC 03729-01127 and AB Cam exhibit period increases , implying fifth and third crossings of the instability strip , respectively , while BD Cas exhibits a period decrease , indicating a second crossing , with possible superposed trends unrelated to binarity .
More importantly , the observed rates of period change confirm theoretical predictions .
The challenges and prospects for future work in this area of research are discussed .