ab + cd = a + b + c + d + 3 ab - a + cd - c = b + d + 3 a(b - 1) + c(d - 1) = (b - 1 + 1) + (d - 1 + 1) + 3 (a - 1)(b - 1) + (c - 1)(d - 1) = 5
Since there is no other condition, so it is no our own wish what case to consider. As I already told that there can be infinite cases, hence we can consider any case of our choice.
Take (a - 1)(b - 1) = 0 and you will get infinite solutions from this case itself