To evaluate the given mathematical expression, we will simply substitute the given value of 'r' into the equation and do the arithmetic.
The given expression is: (5r)/(3*(r-2)). We know that r = -1. Now, let's substitute r = -1 into the equation.
Step 1 - Substituting 'r' with -1
So our equation now becomes: (5*(-1))/(3*(-1 - 2))
Step 2 - Simplify the equation
Now, simplify the above equation to: (-5)/(-3)*(-3)
Since negatives cancel out each other, the equation simplifies further to:
Step 3 - Simplifying abiding by order of operation (Multiplication before addition)
That would be: 5/(-9)
Step 4 - Division
And that equals 0.5555555555555556 when you divide 5 by -9.
So, upon substitution of r = -1 into the given expression, the final result is determined to be approximately 0.5555555555555556.