To solve the equation √2x-2 + 2√2x-3 + √2x+13 + 8√2x-3 = 5, we can simplify it step by step.

Let's start by combining like terms:

√2x-2 + 2√2x-3 + √2x+13 + 8√2x-3 = 5

Rearranging the terms:

√2x-2 + √2x+13 + 2√2x-3 + 8√2x-3 = 5

Now, let's combine the terms with the same radical:

(√2x-2 + √2x+13) + (2√2x-3 + 8√2x-3) = 5

Simplifying each group of terms:

√2x-2 + √2x+13 = 5 - (2√2x-3 + 8√2x-3)

√2x-2 + √2x+13 = 5 - 10√2x-3

Next, let's isolate the radical terms on one side:

√2x-2 - 5 + 10√2x-3 + √2x+13 = 0

Combining like terms:

11√2x-3 + √2x-2 + √2x+13 - 5 = 0

Now, let's simplify further:

11√2x-3 + 2√2x + 11 = 0

Combining like terms:

13√2x-3 + 11 = 0

Subtracting 11 from both sides:

13√2x-3 = -11

Dividing both sides by 13:

√2x-3 = -11/13

Now, let's square both sides to eliminate the square root:

(√2x-3)^2 = (-11/13)^2

2x - 3 = 121/169

Adding 3 to both sides:

2x = 121/169 + 3

2x = 121/169 + 507/169

2x = 628/169

Dividing both sides by 2:

x = 628/338

Simplifying the fraction:

x = 314/169

Therefore, the solution to the equation √2x-2 + 2√2x-3 + √2x+13 + 8√2x-3 = 5 is x = 314/169.