To multiply the given expression, we can use the distributive property.

First, let's multiply the first terms of each binomial:

(2x)(x) = 2x^2

Next, let's multiply the outer terms:

(2x)(-8√x) = -16x√x

Then, let's multiply the inner terms:

(-3√x)(x) = -3x√x

Finally, let's multiply the last terms:

(-3√x)(-8√x) = 24x

Now, let's combine all the terms:

2x^2 - 16x√x - 3x√x + 24x

Simplifying further, we have:

2x^2 - 19x√x + 24x

So, the product of (2x-3√x+5)(x-8√x+2) is 2x^2 - 19x√x + 24x.