\[\begin{array}{*{35}{l}}

x/5\text{ }<\text{ }\left( 3x-2 \right)/4\text{ }-\text{ }\left( 5x-3 \right)/5  \\

x/5\text{ }<\text{ }\left[ 5\left( 3x-2 \right)\text{ }-\text{ }4\left( 5x-3 \right) \right]/4\left( 5 \right)  \\

x/5\text{ }<\text{ }\left[ 15x\text{ }-\text{ }10\text{ }-\text{ }20x\text{ }+\text{ }12 \right]/20  \\

x/5\text{ }<\text{ }\left[ 2\text{ }-\text{ }5x \right]/20  \\

\end{array}\]

Multiplying both the sides by 20 we get,

\[\begin{array}{*{35}{l}}

x/5\text{ }\times \text{ }20\text{ }<\text{ }\left[ 2\text{ }-\text{ }5x \right]/20\text{ }\times \text{ }20  \\

4x\text{ }<\text{ }2\text{ }-\text{ }5x  \\

4x\text{ }+\text{ }5x\text{ }<\text{ }2\text{ }-\text{ }5x\text{ }+\text{ }5x  \\

9x\text{ }<\text{ }2  \\

\end{array}\]

Dividing both sides by 9, we get

\[\begin{array}{*{35}{l}}

9x/9\text{ }<\text{ }2/9  \\

x\text{ }<\text{ }2/9  \\

\end{array}\]

∴ The solution of the given inequation is (-∞, 2/9).