Re-entry permit with a visa

Hey everyone,
I didn’t realize until after entering the Japan but my current visa is single entry only (valid for 5 years) but I do want to go on vacations and holidays outside of the country (for leisure, visiting family). Generally, how difficult is it to obtain the re-entry permit that’s not related to business or visiting family that are not of Japanese decent? It would be amazing to hear what the turnaround time is and the cost if anyone has any experience applying + getting approved/ rejected.

Thanks!