Solution:

For $n \ge 6,$ substitute the recurrence for $x_{n-1}:$ $$x_n = (x_{n-2} - x_{n-3} + x_{n-4} - x_{n-5}) - x_{n-2} + x_{n-3} - x_{n-4} = -x_{n-5}.$$ Hence $x_{n+10} = -x_{n+5} = x_n,$ so the sequence has period $10.$

Since $531,$ $753,$ and $975$ leave remainders $1,$ $3,$ and $5$ upon division by $10,$ we get $x_{531} = x_1 = 211,$ $x_{753} = x_3 = 420,$ and $x_{975} = x_5 = x_4 - x_3 + x_2 - x_1 = 523 - 420 + 375 - 211 = 267.$

The sum is $211 + 420 + 267 = 898.$