5. (10 points) On a cardboard, the natural numbers $100$, $200$, and $400$ are written. Two more natural numbers are then written, and from these five numbers, several (at least two) are selected to perform arithmetic operations involving only addition and subtraction. In one arithmetic expression, the selected numbers can only appear once. After all such operations, $k$ different non-zero natural numbers can be obtained. What is the maximum value of $k$?
【Analysis】This problem is a variation of the weight measurement problem with weights placed on both ends of a balance. (1) Originally, three numbers can measure up to 6 different weights; (2) Adding another weight $A$, the maximum is $6 \times 3=18$ kinds. Additionally, the sum and difference combinations with 400 yield 2 kinds, totaling 20 kinds; (3) Adding a second weight $B$, the solution is the same as (2). According to this, solve the problem.

【Solution】Solution: (1) $100, 200, 400$ can measure up to 6 different weights: 100, 200, 300, 500, 600, 700;
(2) Adding another weight $A$, there are three scenarios: not placing it, placing it on the left, or placing it on the right, the maximum is: $6 \times 3=18$ kinds; Additionally, the sum and difference combinations with 400 yield 2 kinds, totaling 20 kinds;
(3) Adding a second weight $B$, similarly, the maximum is: $20 \times 3=60$ kinds; The sum and difference combinations with $400, A$ yield 4 kinds, totaling 64 kinds.

Answer: The maximum value of $k$ is 64.