1. The problem is to verify if $x=\frac{1}{2}$ is a root of the polynomial $P(x) = 3x + 2x + 5 = 0$.\n\n2. First, simplify the polynomial by combining like terms: $$P(x) = 3x + 2x + 5 = 5x + 5.$$\n\n3. Substitute $x = \frac{1}{2}$ into the simplified polynomial: $$P\left(\frac{1}{2}\right) = 5\left(\frac{1}{2}\right) + 5 = \frac{5}{2} + 5 = \frac{5}{2} + \frac{10}{2} = \frac{15}{2}.$$\n\n4. Since $P\left(\frac{1}{2}\right) = \frac{15}{2} \neq 0$, $x=\frac{1}{2}$ is not a root of the polynomial.\n\nFinal answer: $x=\frac{1}{2}$ is not a solution to $3x+2x+5=0$.