You can use substring method on String like this..

String myString = 'abcdefghijklmnopqrstuvwxyz';
String smallString = myString.substring(0,5); //<-- this string will be abcde

For a specific use case, lets say if you want maximum of 30 characters no matter the number of words in the resulting string, then you could write a function like this..

String smallSentence(String bigSentence){
  if(bigSentence.length > 30){
    return bigSentence.substring(0,30) + '...';
  }
  else{
    return bigSentence;
  }
}

If the requirement is to specifically get the first few words, lets say first 6 words no matter the resulting string's length, then you could write a function like below. We will also need to use indexOf method on String.

String firstFewWords(String bigSentence){
  
  int startIndex = 0, indexOfSpace;
  
  for(int i = 0; i < 6; i++){
    indexOfSpace = bigSentence.indexOf(' ', startIndex);
    if(indexOfSpace == -1){     //-1 is when character is not found
      return bigSentence;
    }
    startIndex = indexOfSpace + 1;
  }
  
  return bigSentence.substring(0, indexOfSpace) + '...';
}

Additional Edit for creating extension -

You can create an extension on String like so

extension PowerString on String {

  String smallSentence() {
    if (this.length > 30) {
      return this.substring(0, 30) + '...';
    } else {
      return this;
    }
  }

  String firstFewWords() {
    int startIndex = 0, indexOfSpace;

    for (int i = 0; i < 6; i++) {
      indexOfSpace = this.indexOf(' ', startIndex);
      if (indexOfSpace == -1) {
        //-1 is when character is not found
        return this;
      }
      startIndex = indexOfSpace + 1;
    }

    return this.substring(0, indexOfSpace) + '...';
  }
}

And use it like this

  String bigText = 'very big text';
  
  print(bigText.smallSentence());
  print(bigText.firstFewWords());

A. Easy Way

To Split String, we are required to have several steps :

1. Turn it to List

2. Make New Smaller List

3. Transform it back to String

Step 1

To turn String into List, we can use this

String bigSentence = 'Lorem Ipsum is'
bigSentence.split(" ")
// ["Lorem", "Ipsum", "is"]

Step 2

Make New Smaller List, for example get first two words,

we use sublist

List<String> splitted = ["Lorem", "Ipsum", "is"]
splitted.sublist(0, 2)
// ["Lorem", "Ipsum"]

Step 3

Transform it back to String

List<String> smaller = ["Lorem", "Ipsum"]
smaller.join(" ")
// "Lorem Ipsum"

Full Functional Code

at the end, we can simplify it to single line of code

String getFirstWords(String sentence, int wordCounts) {
  return sentence.split(" ").sublist(0, wordCounts).join(" ");
}

String bigSentence = '''
Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book
''';

main() {
  String result = getFirstWords(bigSentence, 2);
  print(result); // Lorem Ipsum


  String resultDots = getFirstWords(bigSentence, 2) + " ...";
  print(resultDots); // Lorem Ipsum ...


}

Alternatives

Actually, there is another options to achive New Smaller List as suggested in Step 2

List<String> splitted = ["Lorem", "Ipsum", "is"]
splitted.take(2)
// ["Lorem", "Ipsum"]

B. Hard Way

As suggested by scrimau, the first method above may experience performance hit by its inefficiency splitting maybe thousands of words at first, in order to get several words.

I just learned that Dart has Runes, that may helps us in this case.

To iterate String, firstly we need to transform it into Runes. As stated here, Runes has iterable

We need to have several steps :

1. Validate find Count

  if (findCount < 1) {
    return '';
  }

2. Turn Separator and Sentence into Runes

  Runes spaceRunes = Runes(wordSeparator);
  Runes sentenceRunes = Runes(sentence);

3. Prepare Final String

  String finalString = "";

4. Iterate Runes

The most important part is here, for your case, we need to find Space ' '

So, later if we already found enough space, we just return the Final String

If we have not found enough space, iterate more and append then Final String

Also note here, we use .single, so the word separator must be single character only.

  for (int letter in sentenceRunes) {
    // <------ SPACE Character IS FOUND----->
    if (letter == spaceRunes.single) {
      findCount -= 1;
      if (findCount < 1) {
        return finalString;
      }
    }
    // <------ NON-SPACE Character IS FOUND ----->
    finalString += String.fromCharCode(letter);
  }

Full Functional Code

String bigSentence = '''
Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book
''';

String getFirstWordsFast(String sentence, String wordSeparator, int findCount) {
  if (findCount < 1) {
    return '';
  }

  Runes spaceRunes = Runes(wordSeparator);
  Runes sentenceRunes = Runes(sentence);
  String finalString = "";

  for (int letter in sentenceRunes) {
    if (letter == spaceRunes.single) {
      findCount -= 1;
      if (findCount < 1) {
        return finalString;
      }
    }
    finalString += String.fromCharCode(letter);
  }
  return finalString;
}

main() {
  String shorterString = getFirstWordsFast(bigSentence, " ", 5);
  print(shorterString); // Lorem Ipsum is simply dummy
}

void main() {
  String bigSentence =
      "Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book";
  
  /// if length of string is greater than 6 words then append dots
  bool appendDots = false;
  
  
  /// this will split string into words
  List<String> tempList = bigSentence.split(" ");

  int start = 0;
  int end = tempList.length;
  /// extract first 6 words
  if (end > 6) {
    end = 6;
    appendDots = true;
  }
  /// sublist of tempList
  final selectedWords = tempList.sublist(start, end);
  /// join the list with space
  String output = selectedWords.join(" ");

   if(appendDots){
     output += "....";
   }
  
  print(output);
}

Edit : Another Solution

Text('Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry\'s standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book',
   maxLines : 1,
   overflow: TextOverflow.ellipsis, 
),

  String sentence = "My single Sentence";
  print(sentence.split(" "));

Try using split(" ") and assign it to a variable and then you can get the first word.

String sampleText = "Lorem ipsum";

sampleText.split(" ").elementAt(0) // Lorem
sampleText.split(" ").elementAt(1) // ipsum

Had the same task, made an extension that truncate whole words with required length and add to the end the suffix.

/// turuncate the [String] without cutting words. The length is calculated with the suffix.
extension Truncate on String {
  String truncate({required int max, String suffix = ''}) {
    return length < max
        ? this
        : '${substring(0, substring(0, max - suffix.length).lastIndexOf(" "))}$suffix';
  }
}

An example how to use

print('hello world two times!'.truncate(max: 15, suffix: '...'));

the result is hello world...