Final answer:
Mrs. Kudra invested $400 at the 5% interest rate.
Step-by-step explanation:
To solve this problem, we can set up a system of equations. Let x represent the amount invested at 5% and y represent the amount invested at 6.5%. From the given information, we know that x + y = $1000 and 0.05x + 0.065y = $59. Solving this system of equations yields x = $400. Therefore, $400 was invested at the 5% interest rate.