Rational equation

Multiplying through by $20$ gives:

$4x+5=10x$

$6x=5$

$\boxed{\boxed{x=\dfrac{5}{6}}}$

Long solution with clear steps:

$\large\begin{aligned} & & \frac { x }{ 5 } +\frac { 1 }{ 4 } & = & \frac { x }{ 2 } \\ \Longrightarrow & & \frac { 4\left( x \right) }{ 4\left( 5 \right) } +\frac { 5\left( 1 \right) }{ 5\left( 4 \right) } & = & \frac { x }{ 2 } \\ \Longrightarrow & & \frac { 4x }{ 20 } +\frac { 5 }{ 20 } & = & \frac { x }{ 2 } \\ \Longrightarrow & & \frac { 4x+5 }{ 20 } & = & \frac { x }{ 2 } \\ \Longrightarrow & & \cfrac { 4x+5 }{ \frac { 20 }{ 2 } } & = & \cfrac { x }{ \frac { 2 }{ 2 } } \\ \Longrightarrow & & \frac { 4x+5 }{ 10 } & = & x \\ \Longrightarrow & & \frac { 4x+5 }{ 10 } \times 10 & = & 10x \\ \Longrightarrow & & 4x+5 & = & 10x \\ \Longrightarrow & & 5 & = & 10x-4x \\ \Longrightarrow & & 6x & = & 5 \\ \therefore & & x & = & \boxed { \boxed { \frac { 5 }{ 6 } } } \end{aligned}$