Is the prayer considered valid and purity achieved if menstruation occurs every five days with an IUD?

The minimum period of purity between two menstrual cycles is thirteen days according to the Hanbalis, or fifteen days according to the majority of scholars. Therefore, if the blood returns after five days, it cannot be considered a new menstrual period due to not reaching the minimum period of purity. If the blood comes every five days, the total duration of the bleeding and the intervening periods of purity exceeds fifteen days (the maximum duration of menstruation), which means you are experiencing irregular bleeding (istihada). In this case, you must refer to your previous regular period if you know it, or apply the criterion of distinguishing (between menstrual and non-menstrual blood), or consider six or seven days of the month as menstruation by estimation and what is beyond that as irregular bleeding.