Given f g(x) = (x+2)/(3) and g(x) = 2x+5.

Given $f \circ g(x) = \frac{x+2}{3}$ and $g(x) = 2x+5$.
The notation $f \circ g(x)$ means $f(g(x))$.
So, we have:

$$f(g(x)) = \frac{x+2}{3}$$

Let $u = 2x+5$. We need to express $x$ in terms of $u$.

$$u = 2x+5$$ $$u-5 = 2x$$ $$x = \frac{u-5}{2}$$

Now substitute this expression for $x$ into the equation for $f(2x+5)$:

$$f(u) = \frac{\left(\frac{u-5}{2}\right)+2}{3}$$

Simplify the numerator:

$$f(u) = \frac{\frac{u-5+4}{2}}{3}$$ $$f(u) = \frac{\frac{u-1}{2}}{3}$$ $$f(u) = \frac{u-1}{6}$$

Replacing $u$ with $x$, we get the function $f(x)$:

$$f(x) = \frac{x-1}{6}$$

Substitute $(x+1)$ into the expression for $f(x)$:

$$f(x+1) = \frac{(x+1)-1}{6}$$ $$f(x+1) = \frac{x}{6}$$

The value of $f(x+1)$ is $\boxed{\frac{x}{6}}$.