prefer a column value over another in rows that has two same max value

Question

    c1        c2              c3         c4      c5
    "97"    "12078602701"   "ANSWERED"  "334"   "TIMECONDITION_16"  
    "98"    "12078602701"   "ANSWERED"  "334"   "333"   
    "105"   "12078602702"   "ANSWERED"  "334"   "TIMECONDITION_16"  
    "106"   "12078602702"   "ANSWERED"  "334"   "333"   
    "111"   "14126061978"   "ANSWERED"  "279"   "TIMECONDITION_16"
    "113"   "14126061978"   "ANSWERED"  "279"   "265"   
    "120"   "12078602703"   "ANSWERED"  "334"   "TIMECONDITION_16"
    "121"   "12078602703"   "ANSWERED"  "334"   "333"   
    "131"   "12103306549"   "NO ANSWER" "13"    "TIMECONDITION_16"
    "135"   "12078602704"   "ANSWERED"  "334"   "TIMECONDITION_16"
    "136"   "12078602704"   "ANSWERED"  "334"   "333"   

Consider the above rows in which it needs to be grouped by c2 and we have to give preference to column 5 value not having 'timecondition_16' but if no other value exists other than TIMECONDITION_16 only on that condition it should include row with TIMECONDITION_16. the expected result is

"98"    "12078602701"   "ANSWERED"  "334"   "333"   
"106"   "12078602702"   "ANSWERED"  "334"   "333"   
"113"   "14126061978"   "ANSWERED"  "279"   "265"   
"121"   "12078602703"   "ANSWERED"  "334"   "333"   
"131"   "12103306549"   "NO ANSWER" "13"    "TIMECONDITION_16"
"136"   "12078602704"   "ANSWERED"  "334"   "333"   

Answer 1

With NOT EXISTS :

select t.* from tablename t
where c5 <> 'TIMECONDITION_16'
or not exists (
   select 1 from tablename
   where c2 = t.c2 and c5 <> 'TIMECONDITION_16'
)

See the demo .
Results:

| c1  | c2          | c3        | c4  | c5               |
| --- | ----------- | --------- | --- | ---------------- |
| 98  | 12078602701 | ANSWERED  | 334 | 333              |
| 106 | 12078602702 | ANSWERED  | 334 | 333              |
| 113 | 14126061978 | ANSWERED  | 279 | 265              |
| 121 | 12078602703 | ANSWERED  | 334 | 333              |
| 131 | 12103306549 | NO ANSWER | 13  | TIMECONDITION_16 |
| 136 | 12078602704 | ANSWERED  | 334 | 333              |

Answer 2

In MySQL 8 you can use row_number() . Partition by c2 and order by the Boolean expression c5 = 'TIMECONDITION_16' . Each row for which this is true will come after all rows for which this is false as true is interpreted as 1 and false as 0 in that context. Filter for all rows where the row_number() is 1. (You didn't specify any second criteria for the ordering so other than putting 'TIMECONDITION_16' last a random row will be chosen.)

SELECT x.c1,
       x.c2,
       x.c3,
       x.c4,
       x.c5
       FROM (SELECT t.c1,
                    t.c2,
                    t.c3,
                    t.c4,
                    t.c5,
                    row_number() OVER (PARTITION BY t.c2
                                       ORDER BY t.c5 = 'TIMECONDITION_16') rn
                    FROM elbat t) x
       WHERE x.rn = 1;

db<>fiddle