To simplify the expression \(5\left(0.5k - 1\right) + 2\left(0.4 - k\right)\), we will distribute the constants and then combine like terms.
First, distribute \(5\) in the first term:
\[ 5\left(0.5k - 1\right) = 5 \cdot 0.5k - 5 \cdot 1 = 2.5k - 5 \]
Next, distribute \(2\) in the second term:
\[ 2\left(0.4 - k\right) = 2 \cdot 0.4 - 2 \cdot k = 0.8 - 2k \]
Now combine both parts:
\[ 2.5k - 5 + 0.8 - 2k \]
Next, combine the \(k\) terms and the constant terms:
\[ (2.5k - 2k) + (-5 + 0.8) = 0.5k - 4.2 \]
Thus, the final simplified expression is:
\[ 0.5k - 4.2 \]