1) To solve for x in the equation 10x + 17 = 5x + 92, first subtract 5x from both sides:
10x + 17 - 5x = 5x + 92 - 5x
5x + 17 = 92
Next, subtract 17 from both sides:
5x + 17 - 17 = 92 - 17
5x = 75
Finally, divide by 5 to solve for x:
5x / 5 = 75 / 5
x = 15

Therefore, the solution to the equation 10x + 17 = 5x + 92 is x = 15.

2) To solve for x in the equation 5(x-2) = 4(x+1) + 10, first distribute the coefficients:
5x - 10 = 4x + 4 + 10
Next, combine like terms:
5x - 10 = 4x + 14
Subtract 4x from both sides:
5x - 4x - 10 = 4x - 4x + 14
x - 10 = 14
Then, add 10 to both sides:
x - 10 + 10 = 14 + 10
x = 24

Therefore, the solution to the equation 5(x-2) = 4(x+1) + 10 is x = 24.