MySQL 8.0

By using db<>fiddle, you agree to license everything you submit by Creative Commons CC0.
create table bedrock (
  id int primary key auto_increment, 
  position int not null, 
  name varchar(30) not null
);
insert into  bedrock (position, name) values
(5, 'Fred'),
(3, 'Wilma'),
(1, 'Betty'),
(2, 'Barney'),
(4, 'Pebbles');

Records: 5  Duplicates: 0  Warnings: 0


select * from bedrock order by position;


id
position
name


3
1
Betty

4
2
Barney

2
3
Wilma

5
4
Pebbles

1
5
Fred


update bedrock
join
(
  select pos_from, pos_to, 
  case when pos_to > pos_from then pos_from else pos_to end as pos_min,
  case when pos_to > pos_from then pos_to else pos_from end as pos_max,
  case when pos_to > pos_from then -1 else 1 end as pos_delta
  from (
    select 
    5 as pos_from, 
    3 as pos_to
  ) q1
) q2 on position between pos_min and pos_max
set position = case 
               when position = pos_from 
               then pos_to 
               else position + pos_delta 
               end;

Rows matched: 3  Changed: 3  Warnings: 0


select * from bedrock order by position;


id
position
name


3
1
Betty

4
2
Barney

1
3
Fred

2
4
Wilma

5
5
Pebbles