To evaluate the expression \( 3|a| + 5|b| \) given \( a = -2 \) and \( b = -1 \), we first find the absolute values of \( a \) and \( b \):
\[ |a| = |-2| = 2 \] \[ |b| = |-1| = 1 \]
Next, we substitute these values into the expression:
\[ 3|a| + 5|b| = 3(2) + 5(1) \]
Now, we perform the multiplication:
\[ 3(2) = 6 \] \[ 5(1) = 5 \]
Finally, we add these results together:
\[ 6 + 5 = 11 \]
Thus, the value of \( 3|a| + 5|b| \) is \( \boxed{11} \).