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5\sqrt{3}-\sqrt{192}
Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.
5\sqrt{3}-8\sqrt{3}
Factor 192=8^{2}\times 3. Rewrite the square root of the product \sqrt{8^{2}\times 3} as the product of square roots \sqrt{8^{2}}\sqrt{3}. Take the square root of 8^{2}.
-3\sqrt{3}
Combine 5\sqrt{3} and -8\sqrt{3} to get -3\sqrt{3}.