If you truly cannot play this chord, then you always have the option of rolling the chord, or of leaving one note out.
However, I suggest you try this first:1. Play the EE octave and see how your other fingers []naturally[] fall on the G# and C#. Personally I find 5421 more comfortable.
2. Now for stretching. Understand this basic principle and you will not need stratching exercises or anything. Here is the principle:a. Try to open your fingers 2 - 3 as wide as they will go. You will notice that a lot of effort may result in a bery small opening. b. Now, try to do it again, but this time, instead of using your muscles, use the other hand to do it. You will see that as long as your fingers are passive and relaxed you will be able to stretch a lot more than in a above.
c. From a and b above you have the obvious conclusion: in order to stretch your fingers withou too much discomfort, you need to do it passively, that is, an external agent must stratch your fingers for you. Now, you cannot use your other hand to stretch your fingers to reach the C# and G#, (although I guess you could bring someone to do it for you, just like a page turner, you could have a finger-stretcher ), so you must use the keys themselves to stretch your fingers. It is dificult to describe this in writing, but I trust you will catch my drift. Let us say you are using 5321. Playing the EE octave is not a problem. Now place the 2nd finger on the C# and anchor it on the key 9this is easy as the balck keys are above the keyboard), and then "push" your hand towards the left (without any help from the finger abductors) and you should be able to manage the stretchwithout undue stress.
I hope this helps.