To solve the equation |4x-3|+2=5x, we need to consider two cases: when 4x-3 is positive and when it is negative.

Case 1: 4x-3 is positive
In this case, the equation becomes (4x-3)+2=5x
Simplifying, we get 4x-3+2=5x
Combining like terms, we have 4x-1=5x
Subtracting 4x from both sides, we get -1=x

Case 2: 4x-3 is negative
In this case, the equation becomes -(4x-3)+2=5x
Simplifying, we get -4x+3+2=5x
Combining like terms, we have -4x+5=5x
Adding 4x to both sides, we get 5=9x
Dividing both sides by 9, we get x=5/9

Therefore, the solutions to the equation |4x-3|+2=5x are x=-1 and x=5/9.