Let the digit at unit’s place be a and ten’s place be b. Thus, the number to be found is $10b+a$.
From given question, the sum of two digit number is equal to $5$.
Thus we can write equation according to question,
$a+b=5$ ………….. (i)
On interchanging the place of digits, the new number so formed will be $10a+b$.
It is also given in question that, the new number obtained after interchanging the digits is greater by $9$ from the original number.
Therefore, this can be written as;
$10a+b=10a+b+9$
⇒ $10a+b–10b–a=9$
⇒ $9a–9b=9$
⇒ $9(a–b)=9$
⇒ $a–b=1$………………. (ii)
On solving (i) and (ii), we get value of a and b
Adding the eq. (i) and (ii), we get;
$(a+b)+(a–b)=5+1$
⇒ $a+b+a–b=5+1$
⇒ $2a=6$
⇒ $a=6/2$
⇒ $a=3$
Putting the value of a in the equation (i), we get;
$3+b=5$
⇒ $b=5-3$
⇒ $b=2$
Thus, the required number is $10\times 2+3=23$