If the seating order around each table does not matter, this problem boils down to the number of ways that 5 people can be chosen from a group of 10 people. The short way of saying this is: "ten choose five".
The logic here is that once the first table is selected, the remaining people must go to the second table.
This number is the combinatorial coefficient 10!/[ 5! (10-5)!] (x! denotes x factorial)
This evaluates to 252
If the seating order around a table does matter this number must be multiplied by the number of circular permutations of 5. This number is 4! = 24. In fact, one must multiply by 24 twice, once for each table.
So if the seating order does matter, then the answer is 252 x 24 x24 = 145152