To simplify this expression, we first distribute the 1/2 to the terms inside the parentheses:

1/2(x^2) + 1/2(x) - 5/2 + lg5x + lg(1/5)x

Next, we can combine like terms by adding the terms:

1/2(x^2) + 1/2(x) - 5/2 + lg(5x/1/5x)

Now, we simplify the logarithmic term by using the properties of logarithms:

= 1/2(x^2) + 1/2(x) - 5/2 + lg(25)

Therefore, the simplified expression is 1/2(x^2) + 1/2(x) - 5/2 + lg(25).