If $$z = 2 + 3i$$, then $$z^5 + \bar{z}^5$$ is equal to:

We have $$z = 2 + 3i$$, so $$\bar{z} = 2 - 3i$$. We need to compute $$z^5 + \bar{z}^5$$. Since $$\bar{z}^5 = \overline{z^5}$$, we know that $$z^5 + \bar{z}^5 = 2\,\text{Re}(z^5)$$. So we just need the real part of $$z^5$$.

We compute successive powers of $$z$$:

$$z^2 = (2 + 3i)^2 = 4 + 12i + 9i^2 = 4 + 12i - 9 = -5 + 12i$$

$$z^3 = z \cdot z^2 = (2 + 3i)(-5 + 12i) = -10 + 24i - 15i + 36i^2 = -10 + 9i - 36 = -46 + 9i$$

$$z^4 = z \cdot z^3 = (2 + 3i)(-46 + 9i) = -92 + 18i - 138i + 27i^2 = -92 - 120i - 27 = -119 - 120i$$

$$z^5 = z \cdot z^4 = (2 + 3i)(-119 - 120i) = -238 - 240i - 357i - 360i^2 = -238 - 597i + 360 = 122 - 597i$$

Now, $$\text{Re}(z^5) = 122$$, so $$z^5 + \bar{z}^5 = 2 \times 122 = 244$$.

Hence, the correct answer is Option A.