Letter Changes coderbyte
DRY (Don't Repeat Yourself)

You have a list of else if statements that all do the same thing. JavaScript has the .toUpperCase method so hardcoding character codes to perform capitalization is unnecessary. You can do newString += str[i].toUpperCase().  

Use variables for constant values

Instead of constant values directly in your code, use a variable to store them. You know you want to capitalize vowels, so you can create an array var vowels = ['a', 'e', 'i', 'o', 'u'] to store your constants. This makes it easier to modify in the future - like if the requirements changed and now y is a vowel.

Putting these two together, your capitalization code can be pretty concise:

// vowels.indexOf(str[i]) !== -1 would work, too
if(vowels.includes(str[i]){ 
  newString += str[i].toUpperCase();
}