Another approach to use Reminder Theorem
We have to find last two digits so when we divide a number by 100 we got reminder which are last two digits.
Using this concept we can find as
$\Phi (100) = 40$ (Euler totient function)
$245 mod 40 = 5$
Now we can easily handle given number
$7^5 mod 100 = 07$
Hence last two digits are 07