MySQL 8.0

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CREATE TABLE forms (
  `id` INTEGER,
  `order` INTEGER
);

INSERT INTO forms
  (`id`, `order`)
VALUES
  ('1', '0'),
  ('2', '1'),
  ('3', '2'),
  ('4', '3'),
  ('5', '4');

Records: 5  Duplicates: 0  Warnings: 0


UPDATE forms f
CROSS JOIN (SELECT `order` FROM forms WHERE id = 5) c
INNER JOIN (
  SELECT *, ROW_NUMBER() OVER (ORDER BY `order`) rn
  FROM forms
  WHERE `order` > -1 and `order` <= 4 
) t ON t.id = f.id
SET f.`order` = c.`order` + t.rn;

Rows matched: 5  Changed: 5  Warnings: 0


SELECT * FROM forms;


id
order


1
5

2
6

3
7

4
8

5
9