Find the x-coordinate of the turning point using the formula x = -(b)/(2a).

For $y = x^2 + x + c$, we have $a=1$, $b=1$.

$$x = -\frac{1}{2(1)} = -\frac{1}{2}$$

$$y = \left(-\frac{1}{2}\right)^2 + \left(-\frac{1}{2}\right) + c$$ $$y = \frac{1}{4} - \frac{1}{2} + c$$ $$y = \frac{1}{4} - \frac{2}{4} + c$$ $$y = -\frac{1}{4} + c$$

The turning point is $\boxed{\left(-\frac{1}{2}, c - \frac{1}{4}\right)}$.

For $y = 3x^2 - 4x + 5$, we have $a=3$, $b=-4$.

$$x = -\frac{(-4)}{2(3)} = \frac{4}{6} = \frac{2}{3}$$

$$y = 3\left(\frac{2}{3}\right)^2 - 4\left(\frac{2}{3}\right) + 5$$ $$y = 3\left(\frac{4}{9}\right) - \frac{8}{3} + 5$$ $$y = \frac{12}{9} - \frac{8}{3} + 5$$ $$y = \frac{4}{3} - \frac{8}{3} + \frac{15}{3}$$ $$y = \frac{4 - 8 + 15}{3}$$ $$y = \frac{11}{3}$$

The turning point is $\boxed{\left(\frac{2}{3}, \frac{11}{3}\right)}$.