What is the smallest symmetrical number greater than 56,789 which is exactly divisible by 7?

The number has to be form

10000x+1000y+100z+10y+z
= 10001x+ 1010y + 100z

10001x + 1010y+100z mod 7 = 5x + 2y + 2z mod 7

x cannot be < 5. so let x = 5 and let us look for solution y minimum 6

so 25+2y+2z mod 7 = 0 or 2y+2z = 3 mod 7 or y + z = 5 mod 7

y+z = 5 no solution
so y + z = 12 if y = 6 z = 6 not possible

so y = 7 and z = 5 possible

number = 57575

it is 7 * 8225
if we did not find a solution with x = 5 then we should have tried at x = 6