If you've ever had an Apple ID, you still have one. You should visit iforgot.apple.com, put in the (non-Apple) email address you have, and then you will be prompted on how to reset your password.
Remember that once you reset your password, all your other Apple devices will prompt you to re-sign in to iCloud and any other Apple Services you have with your new password. If you have two-factor authentication turned on, you will get verification codes on your iPhone 5s.
Finally, I should point out that your iPhone 5s is no longer supported and cannot use the most recent iOS updates, so it is only a matter of time before certain apps and services being becoming non-functional you will want to be looking for a replacement iPhone in the near future. The iPhone SE (2020) is an excellent upgrade, and depending on your cellular provider and current plan may be a very inexpensive option.