Here's what you're looking for:

const txt = "lorem ipsum and dolor and sit or amet consecteturand elit";

console.log(txt.split(/ and | or /));

1. You can use this regexp:

const text = "test1 test2 and test2 or test4 test5";
const regexp = /(?<=^|and |or ).*?(?= and| or|$)/g;

console.log(text.match(regexp));

P.S. But keep in mind that positive lookbehind feature is not supported in all browsers

2. You can use this regexp which will not ignore all empty spaces around need parts:

const text = "   test1 test2    and    test2    or    test4 test5   ";
const regexp = /\s*(?!and|or)\b.*?(?=and|or|$)/g;

console.log(text.match(regexp));

3. You can use this regexp which will ignore all empty spaces around need parts:

const text = "    test1 test2    and    test2    or    test4 test5     ";
const regexp = /(?!and|or|\s)\b.*?(?=\s*(and|or|$))/g;

console.log(text.match(regexp));

I would probably just do the obvious:

const rxWords = /\S+/g;
const rxConnectors = /^(and|or)$/i;
const nonConnector = w => ! rxConnectors.test(w) ;

function getInterestingWords( s ) {
  const corpus  = s ?? '' ;
  const matches = corpus.match( rxWords ) ;
  const words   = matches.filter( nonConnector ) ;

  return words;
}

Given that, executing

const text = 'test1 test2 and test2 or test4 test5f' ;
const interestingWords = getInterestingWords(text);

sets interestingWords to the expected

[ 'test1', 'test2', 'test2', 'test4', 'test5' ]