Let's solve the equations one by one.

### Equation g:
\[
x - \frac{1}{3} = \frac{5}{6}
\]
To isolate \( x \), we can add \(\frac{1}{3}\) to both sides:

\[
x = \frac{5}{6} + \frac{1}{3}
\]
To add the fractions, we need a common denominator, which is 6:

\[
\frac{1}{3} = \frac{2}{6}
\]
So,

\[
x = \frac{5}{6} + \frac{2}{6} = \frac{7}{6}
\]

### Equation i:
\[
(2x + 3)^2 = 25
\]
Taking the square root of both sides gives us two cases:

\[
2x + 3 = 5 \quad \text{or} \quad 2x + 3 = -5
\]

**Case 1**: \( 2x + 3 = 5 \)

\[
2x = 5 - 3 \implies 2x = 2 \implies x = 1
\]

**Case 2**: \( 2x + 3 = -5 \)

\[
2x = -5 - 3 \implies 2x = -8 \implies x = -4
\]

So the solutions for this equation are \( x = 1 \) or \( x = -4 \).

### Equation h:
\[
x : \left( \frac{3}{2} \right)^9 = \left( \frac{3}{2} \right)^3
\]
This equation can be rewritten using equality of the bases:

\[
x = \left( \frac{3}{2} \right)^9 \div \left( \frac{3}{2} \right)^3 = \left( \frac{3}{2} \right)^{9-3}
\]
Thus,

\[
x = \left( \frac{3}{2} \right)^6
\]

### Summary of Solutions:
- For equation \( g \): \( x = \frac{7}{6} \)
- For equation \( i \): \( x = 1 \) or \( x = -4 \)
- For equation \( h \): \( x = \left( \frac{3}{2} \right)^6 \)