Let unit digit=y and tens digit=x

So, two digit number = 10x+y

From first statement two digit number is five times the sum of digits.

10x+y=5(x+y)

10x+y=5x+5y

5x-4y=0---------equation 1

After interchanging the digits we have new number as 10y+x.

So, 10x+y=10y+x-9

9x-9y=-9

x-y=-1---------------equation 2.

x=y-1

Plugging x=y-1 in first equation.

5(y-1)-4y=0

5y-5-4y=0

y=5

So, x=y-1=5-1=4

Number= 10x+y=10*4+5=45