The prevalence of the disease entity im stuyding is unknown. So we'll be going back 5 years and see if the data generated is significant enough, if not we'll continue to go further back. (we are going through raw data). Would this be consecutive or sequential sampling?
If you keep increasing your sample size until you find something significant, you are just after significance, which is way too simplistic. With enough data, any difference can be significant.
Defend why you are going up to 5 or x many years. Run a sample calculation: what is the prevalence you are trying to detect (what magnitude of prevalence you believe it's relevant), what is the precision around that estimate that you want to have, what is the confidence interval you want to have, and based on that, you can determine how many observations you need to make. If this is implies that to have this many observations you need to look 2 years back or 10 years it's a matter of how you want your precision of the prevalence estimation to be, and not if "it is significant" or not.
As for nomenclature (consecutive and sequential), usually those terms are used on prospective studies. Your study seem to be retrospective in which you are observing all data that got recorded until X many years back. It's slightly different, and one could argue that there were other cases that for whatever reason simply did not end up being recorded on your registries despite you looking on all (that got recorded). In the end this is nomenclature. While important to use the right terminology, those won't fit all scenarios. Them, it's more important to accurately display your study design - perhaps attaching a label to it can confuse more than plainly explaining what you did.
Simple answer is none.
Your research question either needs more clarification (period prevalence/point prevalence) or it probably requires a different study design.
I believe if you continue sampling until you reach your desired prec-alculated sample size then that is consecutive, but if you stop and then analyse, and then sample , where your sample size is not prefixed then that is sequential.
In consecutive sampling we continue sampling until we reach our desired calculated sample size, but in sequential sampling we stop and then analyse, and then sample , where our sample size is not prefixed
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