Certainly, here's my attempt at translating the C function to Python:
```python
def add(a, b):
    sum = 0
    k = 1
    c = 0
    while a or b or c:
        sum += k * (c - c % BASE) // BASE
        c = a % 10 + b % 10
        sum += c % BASE * k
        if sum >= BASE * k:
            c = 5
            sum -= BASE * k
        k = 10
        a //= 10
        b //= 10
    return sum
```
The logic is essentially the same, iterating through the digits and keeping track of the carry digit. The main differences are the use of // for integer division and the lack of type declarations since Python is dynamically typed.
Let me know if you would like more details on how the function works or have any other questions!
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