Our thousands digit needs to be either 5 or 6.
When our thousands digit is 5, the hundreds digit is from 0 to 4
While if it is 6, the hundreds digit is from 5 to 9.
The tens and ones digit can be any number.
Case 1:
Notice that if we make the thousands digit be 5 and the hundred as 4.
5 + 4 + _ + _ = 26
9 + _ + _ = 26
_ + _ = 17
This means the blanks have values 8 and 9. This means the possible values for this case is 5489 and 5498.
Case 2:
Thousands digit: 5, Hundreds: 3
5 + 3 + _ + _ = 26
_ + _ = 18
The possible value for this case is 5399.
Other Cases when thousands digit is 6:
H:5 - 6569, 6596, 6578, 6587
H:6 - 6695, 6659, 6686, 6668, 6677
H:7 - 6749, 6794, 6785, 6758, 6767, 6776
H:8 - 6839, 6893, 6848, 6884, 6857, 6875, 6866
H:9 - 6929, 6992, 6938, 6983, 6947, 6974, 6956, 6965
