The present age?

Father is 4 times Harini so F=4h.
Father and mother age difference is 5 so
Abs(f-m)=5 so f-m=5 or m-f=5.
3 years ago sum was 70 so
F-3+m-3+h-3=70.
Simplify to f+m+h-15=70 so F+m+h=85 => F+m+f/4=85.
Case 1: mother is older means that.
F+(f+5) +f/4=85 => 9f/4=80 => F=35.5555... Not an integer makes no sense.
Case 2: father is older means that
F+(f-5)+f/4=85 => 9f/4=90 => F=40 which is an integer so the father must be older. Therefore the father is 40 years old.

Let $F$ be the father's age, $M$ be the mother's age and $H$ be Harini's age. Then we have

$F=4H$ $\implies$ $H=\dfrac{F}{4}$ $\color{#D61F06}(1)$

$F-M=5$ $\implies$ $M=F-5$ $\color{#D61F06}(2)$

$F-5+M-5+H-5=70$ $\implies$ $F+M+H=85$ $\color{#D61F06}(3)$

Substitute $\color{#D61F06}(1)$ and $\color{#D61F06}(2)$ in $\color{#D61F06}(3)$ . We have

$F+F-5+\dfrac{F}{4}=85$

$2.25F=90$

$F=40$

suppose,Harini's age=x, her father's age=y=4x, her mother's age=z. now,y-z=5......(1) as the sum of their age was 70 before 5years,now it will be 85.. so,now,we get, x+y+z=85 =>y/4+y+y-5=85 =>y=40 so,her father's present age is40

for present ages => Harini = x .....her father = 4x......her mother = 4x -5 their age 5 years back harini= x -5 ....... her father = 4x-5 ...... her mother = 4x -10... now we get the eq . (x-5)+(4x-5)+(4x-10) = 70 = 10 .........father's age =4x =40