Suppose I have two 5-digit numbers (A and B) and two 50-digit numbers(C and D). Do the operations A+B and C+D have equal complexity in terms of time and space? or C+D is more complex due to the size of digits?
The complexity of arithmetic operations is typically measured in bit operations, though not everybody agrees this is the correct measure. There is a Wikipedia page listing the complexity of the best algorithms currently known for various operations, including addition and multiplication.
Here, complexity refers to the time complexity of performing computations on a multitape Turing machine.
However, for example, if you use a random access machine, the time and space complexity of an arithmetic operation of any-digit numbers is considered to be $O(1)$.