Let's first consider this pattern: [34]{3}
The […] is a character class, it matches exactly one of the characters in the set. The {n} is an exact finite repetition.
So, [34]{3} informally means "exactly 3 of either '3' or '4'". Thus, it matches "333", "334", "343", "344", "433", "434", "443", "444", and nothing else.
As a string literal, the pattern is "[34]{3}". If you don't want to hardcode this pattern, then just generate similar-looking strings that follows this template "[…]{n}". Just put the characters that you want to match in the …, and substitute n with the number you want.
Here's an example:
String alpha = "aeiou";
int n = 5;
String pattern = String.format("[%s]{%s}", alpha, n);
System.out.println(pattern);
// [aeiou]{5}
We've now seen that the pattern is not hardcoded, but rather programmatically generated depending on the values of the variables alpha and n. The pattern [aeiou]{5} will 5 consecutive lowercase vowels, e.g. "ooiae", "ioauu", "eeeee", etc.
It's again not clear if you just want to match these kinds of strings, or if they have to appear like '…'/'…'/'…'/'…'/'…'. If the latter is desired, then simply compose the pattern as desired, using repetition and grouping as necessary. You can also just programmatically copy and paste the pattern 5 times if that's simpler. Here's an example:
String p5 = String.format("'%s'/'%<s'/'%<s'/'%<s'/'%<s'", pattern);
System.out.println(p5);
// '[aeiou]{5}'/'[aeiou]{5}'/'[aeiou]{5}'/'[aeiou]{5}'/'[aeiou]{5}'
This will now match strings like "'aeooi'/'eeiuu'/'uaooo'/'eeeia'/'eieio'".
Caveat
Do be careful about what goes in alpha. Specifically, -, [. ], &&, ^, etc, are special metacharacters in Java character class definition. If you restrict alpha to contain only digits/letters, then you will probably not run into any problems, but e.g. [^a] does NOT mean "either '^' or 'a'". It in fact means "anything but 'a'. See java.util.regex.Pattern for exact character class syntax.