To solve the equation |x+5|= 2x-1, we can split it into two separate equations:

1) x+5 = 2x-1
2) -(x+5) = 2x-1

Let's solve equation 1 first:

x + 5 = 2x - 1

Subtract x from both sides:

5 = x - 1

Add 1 to both sides:

6 = x

So, x = 6 is a solution to equation 1.

Now let's solve equation 2:

-(x+5) = 2x - 1

Distribute the negative sign:

-x - 5 = 2x - 1

Add x to both sides:

-5 = 3x - 1

Add 1 to both sides:

-4 = 3x

Divide both sides by 3:

-4/3 = x

So, x = -4/3 is a solution to equation 2.

Therefore, the solutions to the original equation |x+5|= 2x-1 are x = 6 and x = -4/3.