The tax scheme you mention is the Non Habitual Residency (NHR) scheme, which has now changed so that you pay 10% for 10 years instead of zero. It is not a residence visa. The NHR is open to any foreign national who takes out Portuguese residency. The Golden visa scheme (property investment) only...
The Golden visa scheme is only one option though. You can apply for a D7 residence visa without having to buy a property or make a business investment.
You don't need to wait 5 years to get residency. You can get residency for 5 years with a D7 visa or Golden Visa. After 5 years you can apply for another 10 years or for permanent residency.
Easiest way is to have an Irish grandparent and apply for Irish citizenship by foreign birth. Then you can get an Irish passport and you have the right to residence anywhere in the EU. If that is not possible then you need, generally, around 10,000 euros in the bank and a guaranteed income of...