A Play Store that closes the instant it opens usually has corrupted cache or a bad update of Google Play services. It is practically always fixable without a reset.
- 1Force stop the app: Settings → Apps → Google Play Store → Force stop, then reopen.
- 2Clear its cache and, if needed, its data (Storage inside the same screen).
- 3Clear cache of 'Google Play services' and 'Google Services Framework'.
- 4Uninstall Play Store updates (menu in the app info screen) and reboot.
- 5Check for Android system updates, services mismatches get fixed by system patches.
Tip: Never sideload Play Store APKs from random sites to 'fix' it, the store reinstalls its own updates automatically once working.