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\left(5y-8x\right)\left(5y+8x\right)
Rewrite 25y^{2}-64x^{2} as \left(5y\right)^{2}-\left(8x\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
\left(-8x+5y\right)\left(8x+5y\right)
Reorder the terms.