Use the distributive properties of the limit.
[tex]\displaystyle \lim_{x\to2} h(x) \bigg( 5 f(x) + g(x)\bigg) \\\\ ~~~~~~~~ = \lim_{x\to2} h(x) \cdot \lim_{x\to2} \bigg(5f(x) + g(x)\bigg) \\\\ ~~~~~~~~ = \lim_{x\to2} h(x) \cdot \left(\lim_{x\to2} 5f(x) + \lim_{x\to2} g(x)\right) \\\\ ~~~~~~~~ = \lim_{x\to2} h(x) \cdot \left(5 \lim_{x\to2} f(x) + \lim_{x\to2}g(x)\right) \\\\ ~~~~~~~~ = 2 \cdot (5\cdot4 + (-6)) = \boxed{28}[/tex]
