Its been a while since we performed and update on our site. Would there be any issues upgrading to the latest version from such an old version?
As Pete said - 4.7.12 - 5.1.2 should not cause much concern. If you are able to, I would create a sandbox site, upgrade that site and test to see if it all goes well.
There is one version specific caveat you should know about when upgrading from 4.7.31 to 5.0 Though I am not sure it effects you if you are upgrading directly from 4.7.12 - though maybe someone else can answer that.
Alternatively, if you want to really take it slow, you can find the history of CiviCRM versions on SourceForge - maybe upgrade to an older version first and test.
Not particularly. We have nursed upgrades through from 4.4 and 4.6 (yes we inherit some shockingly old systems occasionally) without significant problems. On that scale 4.7.12 doesn't seem to be 'such an old version'.
If you backup code and db and give it a try and you hit issues then just roll back and come back on here with some details of problems you encounter.
(Edit to incorporate Ramesh's helpful comment)
Refer this link docs.civicrm.org/sysadmin/en/latest/misc/switch-servers also you can refer to docs.civicrm.org/sysadmin/en/latest/upgrade/drupal7