If you want to loop through the array in a circular fashion the modulus % operator is the way to go. If you combine that with the Java 8 streaming API:s the solution can look like this.
int[] myArray = {1, 2, 3, 4, 5}; // Setup the array
int startIndex = 3; // Start index as per the OP's example
int addIndex = 4; // Add as per the OP's example
// Loop via streams - no external looping
IntStream.range(startIndex, startIndex + addIndex)
.map(i -> myArray[i % myArray.length]) // circular loop
.forEach(System.out::println /* Do your stuff */); // do your stuff
For more examples, see this answer