4.\(\frac{x-5}3=\frac{x-3}5\)

Given that,\(\frac{x-5}3=\frac{x-3}5\)
LCM of denominators 3 and 5=15

So, \(\frac{x-5}3×15=\frac{x-3}5×15\quad \)[Multiplying both the sides by 15]

\(\Rightarrow (x-5)×5=(x-3)×3\)

\(\Rightarrow 5x-25 = 3x-9\quad \)[Solving the brackets]

\(\Rightarrow 5x-3x = 25-9\quad \)[Transposing 3x to LHS and 25 to RHS]

\(\Rightarrow 2x = 16\)

\(\Rightarrow x = 16÷2\)[Dividing both the sides by 2]

\(\Rightarrow x = 8\)