Brilli the ant is considering the complexities of a 5-dimensional universe. She wants to count the number of integer points that are distance sqrt(n) away from the origin. Let Tn be the set of ordered 5-tuples of integers (a1,a2,a3,a4,a5) such that a1^2+a2^2+a3^2+a4^2+a5^2=n.However, being an ant, she doesn't have enough toes to record numbers that are above 10. Let Dn be the units digit of |Tn|.

Determine ∑ from 1 to 5678 of Di.

To solve this problem, we need to calculate the units digit of the cardinality of the set Tn for each value of n from 1 to 5678, and then find the sum of these units digits.

Step 1: Calculate the cardinality of Tn

To find the cardinality of Tn, we need to count the number of 5-tuples (a1, a2, a3, a4, a5) of integers such that a1^2 + a2^2 + a3^2 + a4^2 + a5^2 = n.

Step 2: Determine the units digit of the cardinality |Tn|

Since we are only interested in the units digit, we can use modular arithmetic to simplify the calculation. We will only keep track of the units digit of each sum of squares.

For example, consider the case where n = 1. In this case, the only possible combination is (a1, a2, a3, a4, a5) = (0, 0, 0, 0, 1) since the sum of squares should be equal to 1. Therefore, |T1| = 1, and the units digit of |T1| is 1.

Step 3: Calculate the units digit for each value of n

We will use the following rules to determine the units digit of the sum of squares:

- The sum of two squares ending in 0 has a units digit of 0.
- The sum of two squares ending in 1 has a units digit of 2.
- The sum of two squares ending in 2 has a units digit of 5.
- The sum of two squares ending in 3 has a units digit of 4.
- The sum of two squares ending in 4 has a units digit of 5.
- The sum of two squares ending in 5 has a units digit of 0.

By applying these rules, we can calculate the units digit for each value of n from 1 to 5678.

Step 4: Find the sum of the units digits, ∑ from 1 to 5678 of Di

Finally, sum up all the units digits obtained in step 3 and find the sum ∑ from 1 to 5678 of Di.

Please note that calculating the units digit for each value of n might be time-consuming, especially for larger values of n. Algorithmic optimizations can be applied to reduce the computational complexity if needed.

Keep in mind that the explanation provided is a general framework for solving this problem. Specific implementation details may vary depending on the programming language or tools used.