Solve the Subtraction Problem: 5763 minus 178

We aim to solve $5763$ minus $178$ using vertical subtraction.

First, align the numbers by their place value:
$\begin{array}{c} \phantom{1}5763 \\ -~~178 \\ \hline \end{array}$

Step 1: Start from the rightmost digit (units place).
Units: $3 - 8$: Since $3$ is less than $8$, we need to borrow.

Borrow from the tens place:
The $6$ in the tens becomes $5$ (after borrowing 1), making the units place $13$.

So, $13 - 8 = 5$.

Step 2: Move to the tens place now.
Tens: $5 - 7$: Borrow again because $5$ is less than $7$.

Borrow from the hundreds place:
The $7$ in the hundreds becomes $6$, turning the tens into $15$.

So, $15 - 7 = 8$.

Step 3: Now the hundreds place.
Hundreds: $6 - 1 = 5$ (Simple subtraction, no borrowing needed).

Step 4: Finally, the thousands place, which is direct.
Thousands: $5 - 0 = 5$.

Thus, after all stages of subtraction, the result is:
$\begin{array}{c} \phantom{1}5763 \\ -~~178 \\ \hline ~~~ 5585 \\ \end{array}$

Therefore, the solution to the subtraction problem is $5585$.