Let's solve each of the equations one by one.

1) \((5/5 - 2x)^2 = 1/9\)

First, simplify \(5/5\) to get \(1\), so the equation becomes:
\((1 - 2x)^2 = 1/9\).

Take the square root of both sides:
\(|1 - 2x| = 1/3\).

This gives two equations:
1. \(1 - 2x = 1/3\)
2. \(1 - 2x = -1/3\)

For \(1 - 2x = 1/3\):
\(-2x = 1/3 - 1\)
\(-2x = -2/3\)
\(x = 1/3\).

For \(1 - 2x = -1/3\):
\(-2x = -1/3 - 1\)
\(-2x = -4/3\)
\(x = 2/3\).

Solutions: \(x = 1/3\) and \(x = 2/3\).

2) \((5x - 1/2)^2 = 4/9\)

Take the square root of both sides:
\(|5x - 1/2| = 2/3\).

This gives two equations:
1. \(5x - 1/2 = 2/3\)
2. \(5x - 1/2 = -2/3\)

For \(5x - 1/2 = 2/3\):
\(5x = 2/3 + 1/2\)
\(5x = 4/6 + 3/6\)
\(5x = 7/6\)
\(x = 7/30\).

For \(5x - 1/2 = -2/3\):
\(5x = -2/3 + 1/2\)
\(5x = -4/6 + 3/6\)
\(5x = -1/6\)
\(x = -1/30\).

Solutions: \(x = 7/30\) and \(x = -1/30\).

3) \((5/3 - x)^2 = 25/36\)

Take the square root of both sides:
\(|5/3 - x| = 5/6\).

This gives two equations:
1. \(5/3 - x = 5/6\)
2. \(5/3 - x = -5/6\)

For \(5/3 - x = 5/6\):
\(-x = 5/6 - 5/3\)
\(-x = 5/6 - 10/6\)
\(-x = -5/6\)
\(x = 5/6\).

For \(5/3 - x = -5/6\):
\(-x = -5/6 - 5/3\)
\(-x = -5/6 - 10/6\)
\(-x = -15/6\)
\(x = 15/6 = 5/2\).

Solutions: \(x = 5/6\) and \(x = 5/2\).

4) \((7/3 - 2x)^2 = 25/36\)

Take the square root of both sides:
\(|7/3 - 2x| = 5/6\).

This gives two equations:
1. \(7/3 - 2x = 5/6\)
2. \(7/3 - 2x = -5/6\)

For \(7/3 - 2x = 5/6\):
\(-2x = 5/6 - 7/3\)
\(-2x = 5/6 - 14/6\)
\(-2x = -9/6 = -3/2\)
\(x = 3/4\).

For \(7/3 - 2x = -5/6\):
\(-2x = -5/6 - 7/3\)
\(-2x = -5/6 - 14/6\)
\(-2x = -19/6\)
\(x = 19/12\).

Solutions: \(x = 3/4\) and \(x = 19/12\).

5) \((4/3 - 1/2x)^2 = 1/4\)

Take the square root of both sides:
\(|4/3 - 1/2x| = 1/2\).

This gives two equations:
1. \(4/3 - 1/2x = 1/2\)
2. \(4/3 - 1/2x = -1/2\)

For \(4/3 - 1/2x = 1/2\):
\(-1/2x = 1/2 - 4/3\)
\(-1/2x = 3/6 - 8/6\)
\(-1/2x = -5/6\)
\(x = 5/3\).

For \(4/3 - 1/2x = -1/2\):
\(-1/2x = -1/2 - 4/3\)
\(-1/2x = -3/6 - 8/6\)
\(-1/2x = -11/6\)
\(x = 11/3\).

Solutions: \(x = 5/3\) and \(x = 11/3\).

These are the solutions to each of the given equations.