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user1066
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With[{x = longList[[All, 3]]}, Pick[longList, x, Min[x]]]

(* {{4, 29, 0, 15, 40}, {31, 3, 0, 3, 61}, {86, 12, 0, 13, 54},
    {48, 56, 0, 4, 94}, {19, 94, 0, 56, 28}, {90, 57, 0, 91,51}, 
    {76, 14, 0, 70, 84}} *)

Original Answer

 Pick[longList, longList[[All, 3]], 
  Min[longList[[All, 3]]]] // AbsoluteTiming


(* {0.000064, {{4, 29, 0, 15, 40}, {31, 3, 0, 3, 61}, {86, 12, 0, 13, 
   54}, {48, 56, 0, 4, 94}, {19, 94, 0, 56, 28}, {90, 57, 0, 91, 
   51}, {76, 14, 0, 70, 84}}} *)

Using longlist as defined by @rhermans

longList = RandomInteger[100, {1000,5}];

and

Select[longList, #[[3]] == Min[longList[[All, 3]]] &] == 
  Pick[longList, longList[[All, 3]], Min[longList[[All, 3]]]]

(* True *) 

Pick[longList, longList[[All, 3]], 
  Min[longList[[All, 3]]]] // AbsoluteTiming


(* {0.000064, {{4, 29, 0, 15, 40}, {31, 3, 0, 3, 61}, {86, 12, 0, 13, 
   54}, {48, 56, 0, 4, 94}, {19, 94, 0, 56, 28}, {90, 57, 0, 91, 
   51}, {76, 14, 0, 70, 84}}} *)

Using longlist as defined by @rhermans

longList = RandomInteger[100, {1000,5}];

and

Select[longList, #[[3]] == Min[longList[[All, 3]]] &] == 
  Pick[longList, longList[[All, 3]], Min[longList[[All, 3]]]]

(* True *) 

With[{x = longList[[All, 3]]}, Pick[longList, x, Min[x]]]

(* {{4, 29, 0, 15, 40}, {31, 3, 0, 3, 61}, {86, 12, 0, 13, 54},
    {48, 56, 0, 4, 94}, {19, 94, 0, 56, 28}, {90, 57, 0, 91,51}, 
    {76, 14, 0, 70, 84}} *)

Original Answer

 Pick[longList, longList[[All, 3]], 
  Min[longList[[All, 3]]]] // AbsoluteTiming


(* {0.000064, {{4, 29, 0, 15, 40}, {31, 3, 0, 3, 61}, {86, 12, 0, 13, 
   54}, {48, 56, 0, 4, 94}, {19, 94, 0, 56, 28}, {90, 57, 0, 91, 
   51}, {76, 14, 0, 70, 84}}} *)

Using longlist as defined by @rhermans

longList = RandomInteger[100, {1000,5}];

and

Select[longList, #[[3]] == Min[longList[[All, 3]]] &] == 
  Pick[longList, longList[[All, 3]], Min[longList[[All, 3]]]]

(* True *)
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user1066
user1066
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Pick[longList, longList[[All, 3]], 
  Min[longList[[All, 3]]]] // AbsoluteTiming


(* {0.000064, {{4, 29, 0, 15, 40}, {31, 3, 0, 3, 61}, {86, 12, 0, 13, 
   54}, {48, 56, 0, 4, 94}, {19, 94, 0, 56, 28}, {90, 57, 0, 91, 
   51}, {76, 14, 0, 70, 84}}} *)

Using longlist as defined by @rhermans

longList = RandomInteger[100, {1000,5}];

and

Select[longList, #[[3]] == Min[longList[[All, 3]]] &] == 
  Pick[longList, longList[[All, 3]], Min[longList[[All, 3]]]]

(* True *)