Answer:

Any number, whose digits sum is divisible by 3 having even number or zero at its unit place, will be divisible by 6.

And, any number, whose digits sum is divisible by 9, will be divisible by 9.

The largest number of 5 digits, satisfying above conditions will be 9999a.

There is the only number replacing ‘a’ is zero, satisfying the condition for divisibility with 6 & 9.

Thus, the number will be 99990.