5. \( a^{3}+27 b^{3}= \)

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The expression \( a^3 + 27b^3 \) can be factored using the sum of cubes formula. The sum of cubes formula states that: \[ x^3 + y^3 = (x + y)(x^2 - xy + y^2) \] In this case, we can rewrite \( 27b^3 \) as \( (3b)^3 \). Thus, we can set \( x = a \) and \( y = 3b \). Now we can apply the sum of cubes formula: \[ a^3 + (3b)^3 = (a + 3b)(a^2 - a(3b) + (3b)^2) \] Now, we simplify the second factor: \[ a^2 - 3ab + 9b^2 \] Putting it all together, we have: \[ a^3 + 27b^3 = (a + 3b)(a^2 - 3ab + 9b^2) \] So, the factored form of \( a^3 + 27b^3 \) is: \[ \boxed{(a + 3b)(a^2 - 3ab + 9b^2)} \]