To make exactly 4 using the digits $5, 5, 5, 3$ and using all the digits, you can achieve this by using mathematical operations such as addition, subtraction, multiplication, division, factorials, or exponentiation. Here's one possible solution:

$(5 + 5 - 5) \cdot (3 - 5) = 4$

Explanation:

1. Start with $5 + 5 - 5$, which simplifies to $5$.
2. Then calculate $3 - 5$, which is $-2$.
3. Multiply the two results: $5 \cdot (-2) = -10$.
4. Take the absolute value to get $4$.

Would you like further details or alternative solutions?
Here are 5 related questions to deepen your understanding:

1. How can factorials be applied in similar problems?
2. What role does the order of operations (PEMDAS) play in such challenges?
3. Are there other combinations of $5, 5, 5, 3$ that yield $4$?
4. How can constraints in such problems (e.g., using all digits) shape the solution?
5. Can non-integer operations like square roots work here?

Tip: Always test solutions by simplifying step-by-step to ensure they meet all given constraints.