Find the area bounded by the curve using the change of variables in double integrals

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Here is the equation:

$$ \left(\frac{x}{a}+\frac{y}{b}\right)^5=\frac{\left(x^2y^2\right)}{c^4} $$

I got the general idea but I don't know how to start solving it, therefore I would greatly appreciate if someone could solve and explain it here.

I am very limited on time since there's a lot of pressure from my other courses. Thus, I would really appreciate detailed explanation of how to approach and solve this equation. I am newbie in this sphere and I struggle with finding correct approaches.

Thank you in advance!