My age: $x$

My brother is 3 years older than me: $x+3$

My father is 3 less than 2 times my age: $2 x-3$

My father's age divided by 5 is equal to my brother's age divided by 3: $(2 x-3) / 5=(x+3) / 3$

By cross multiplication:

$5(x+3)=3(2 x-3)$

$5 x+15=6 x-9$

$x=24$

My father's age: $2 \cdot 24-3=48-3=45$