Since it's an incomplete XML, let's use simple string functions.
LOCATE can find a position of a sub-string.
LEFT gets a sub-string from the start till a position.
And from that sub-string the SUBSTRING_INDEX function is handy to get the characters after the final tag.
Example code:
-- test table
drop table if exists YourTable;
create table YourTable (col varchar(1000));
-- Sample data
insert into YourTable (col) values
('UPDATE</transactionType><column><name>prio</name><newValue>5</newValue><oldValue>1</oldValue><newValue>aaa<oldValue>10863321</oldValue></column></row></table></businessObjectChanges>'),
('UPDATE</transactionType><column> <name>prio</name><newValue>51</newValue><oldValue>11</oldValue><newValue>bbb<oldValue>10863321</oldValue></column></row></table></businessObjectChanges>');
-- Query
SELECT
SUBSTRING_INDEX(LEFT(col, LOCATE('</oldValue>', col)-1),'>',-1) AS oldValue,
SUBSTRING_INDEX(LEFT(col, LOCATE('</newValue>', col)-1),'>',-1) AS newValue
FROM YourTable;
Result:
oldValue newValue
1 5
11 51
A test on rextester here
Side-note:
In MySql 8 you could also use REGEXP_SUBSTR for this.
SELECT
REGEXP_SUBSTR(col,'(?<=<oldValue>)[^<>]*(?=</oldValue)',1,1) as oldValue,
REGEXP_SUBSTR(col,'(?<=<newValue>)[^<>]*(?=</newValue>)',1,1) as newValue
FROM YourTable;
A test on db<>fiddle here
(But be silent about it. Some would frown upon you for using regex to parse XML. F.e. here.
But then again, an invalid XML isn't really an XML)