It may be fun to try using a MC14536 (but a MCU may be easier to work with).
From what I can read both the 555 and MC14538 doesn't say anything about accuracy beyond 10 s. For a 1 s pulse the 555 has an accuracy of 1% whereas the MC14538 has an accuracy of 5%. Based on the original problem of just being able to have a pulse of 5 minutes I see no reason to not use a 555. However, there may be other very good reasons to use a MC14538 since it seems to support (as you write) a lot more options on triggering and input/putput handling.
Tayda is www.taydaelectronics.com . They are based in Thailand. I have used them for years and they have never disappointed me. Shipping to Denmark is 7 days.
For long delays, the semiconductor element, be it an IC or discrete components, is not the limiting factor which determines the accuracy, but the tolerance of the capacitor. For short delays, small capacitors can be used, <10nF which can be found down to 1% tolerance. Longer delays will require an electrolytic capacitor, which will have a tolerance of 20% or poorer.
For example, the discrete circuit I posted previously will have a much poorer accuracy than an IC such as the '555 or '4538 for ms delays, because the base-emitter voltage is not perfectly stable, but for 10 second delays or longer, the accuracy will be similar, because the 20% tolerance of the electrolytic capacitor will swamp and variances is base-emitter voltage.
https://www.eevblog.com/forum/beginners/a-one-time-timer/msg1574389/#msg1574389