To solve the inequality:

(sqrt(3) - sqrt(2))^(3 - x) <= (sqrt(3) + sqrt(2))^sqrt(x + 3)

We can first rewrite the inequality in terms of exponents to make it easier to solve:

[(3 - x) log(sqrt(3) - sqrt(2))] <= [sqrt(x + 3) log(sqrt(3) + sqrt(2))]

Now, let's solve the second inequality:

sqrt(9^(sqrt(x))) <= 6 9^x - 5 3^(sqrt(x)) * 3^x

Let y = sqrt(x), then the inequality now becomes:

sqrt(9^y) <= 6 9^(y^2) - 5 3^(y) * 3^(2y)

This simplifies to:

3^y <= 6 9^(y^2) - 5 3^(3y)

Now, let's examine the inequality step by step further.