The constant term in the expansion of $$\left(2x + \frac{1}{x^7} + 3x^2\right)^5$$ is _____.

We need to find the constant term in the expansion of $$\left(2x + \frac{1}{x^7} + 3x^2\right)^5$$.

Using the multinomial theorem, the general term is:

$$\frac{5!}{a!\, b!\, c!} (2x)^a \left(\frac{1}{x^7}\right)^b (3x^2)^c = \frac{5!}{a!\, b!\, c!} \cdot 2^a \cdot 3^c \cdot x^{a - 7b + 2c}$$

where $$a + b + c = 5$$ and $$a, b, c \geq 0$$.

For the constant term, the power of $$x$$ must be zero:

$$a - 7b + 2c = 0$$

We solve the system: $$a + b + c = 5$$ and $$a - 7b + 2c = 0$$.

From the first equation: $$a = 5 - b - c$$. Substituting into the second:

$$5 - b - c - 7b + 2c = 0 \implies 5 - 8b + c = 0 \implies c = 8b - 5$$

For non-negative integers: $$c \geq 0$$ requires $$b \geq 1$$, and $$a = 10 - 9b \geq 0$$ requires $$b \leq 1$$.

So $$b = 1$$, giving $$c = 3$$ and $$a = 1$$.

The constant term is:

$$\frac{5!}{1!\, 1!\, 3!} \cdot 2^1 \cdot 3^3 = \frac{120}{6} \cdot 2 \cdot 27 = 20 \times 54 = 1080$$

The answer is $$\boxed{1080}$$.