All 100 targets have a solution.
\(1 = ( 5 - 4 )^{12 }\)
\(2 = 5 - \frac{ 12 }{ 4 }\)
\(3 = \sqrt{24 - 15 }\)
\(4 = 124 - 5 !\)
\(5 = \frac{ 21 + 4 }{ 5 }\)
\(6 = 1^{24} + 5 \)
\(7 = 14 - 2 - 5 \)
\(8 = \frac{ 12 }{ 4 } + 5 \)
\(9 = 24 - 15 \)
\(10 = \frac{ 4! }{ 12 } \cdot 5 \)
\(11 = 25 - 14 \)
\(12 = ( 5 - 4 ) \cdot 12 \)
\(13 = 12 - 4 + 5 \)
\(14 = \frac{ 52 }{ 4 } + 1 \)
\(15 = \frac{ 12 }{ 4 } \cdot 5 \)
\(16 = 41 - 25 \)
\(17 = 14 - 2 + 5 \)
\(18 = ( 14 - 5 ) \cdot 2 \)
\(19 = 14 + \sqrt{25 }\)
\(20 = 21 + 4 - 5 \)
\(21 = 12 + 4 + 5 \)
\(22 = 142 - 5 !\)
\(23 = 14 \cdot 2 - 5 \)
\(24 = 45 - 21 \)
\(25 = 1^{5} + 24 \)
\(26 = 15 \cdot 2 - 4 \)
\(27 = 42 - 15 \)
\(28 = ( 12 - 5 ) \cdot 4 \)
\(29 = 24 \cdot 1 + 5 \)
\(30 = \frac{ 15 \cdot 4 }{ 2 }\)
\(31 = 2^{4} + 15 \)
\(32 = 4 \cdot 5 + 12 \)
\(33 = 45 - 12 \)
\(34 = 15 \cdot 2 + 4 \)
\(35 = \frac{ 14 }{ 2 } \cdot 5 \)
\(36 = 41 - \sqrt{25 }\)
\(37 = 42 \cdot 1 - 5 \)
\(38 = \frac{ 152 }{ 4 }\)
\(39 = 14 + 25 \)
\(40 = ( 12 - 4 ) \cdot 5 \)
\(41 = 4 \cdot 5 + 21 \)
\(42 = 54 - 12 \)
\(43 = 12 \cdot 4 - 5 \)
\(44 = 41 - 2 + 5 \)
\(45 = ( 2 - 1 ) \cdot 45 \)
\(46 = \sqrt{25} + 41 \)
\(47 = 42 \cdot 1 + 5 \)
\(48 = 41 + 2 + 5 \)
\(49 = 51 + 2 - 4 \)
\(50 = ( 12 - \sqrt{4} ) \cdot 5 \)
\(51 = 2 \cdot 5 + 41 \)
\(52 = ( 15 - 2 ) \cdot 4 \)
\(53 = 12 \cdot 4 + 5 \)
\(54 = ( 2 - 1 ) \cdot 54 \)
\(55 = 52 - 1 + 4 \)
\(56 = 12 \cdot 5 - 4 \)
\(57 = 12 + 45 \)
\(58 = 15 \cdot 4 - 2 \)
\(59 = 2 \cdot 4 + 51 \)
\(60 = ( 14 - 2 ) \cdot 5 \)
\(61 = \frac{ 5! }{ 4 - 2 } + 1 \)
\(62 = 15 \cdot 4 + 2 \)
\(63 = 2 \cdot 4! + 15 \)
\(64 = 12 \cdot 5 + 4 \)
\(65 = 4^{5 - 2} + 1 \)
\(66 = 12 + 54 \)
\(67 = 2^{4} + 51 \)
\(68 = ( 12 + 5 ) \cdot 4 \)
\(69 = 4^{1 + 2} + 5 \)
\(70 = 14 \cdot \sqrt{25 }\)
\(71 = \sqrt{42 \cdot 5! + 1 }\)
\(72 = 14 \cdot 5 + 2 \)
\(73 = 2^{5} + 41 \)
\(74 = \frac{ 5! }{ 2 } + 14 \)
\(75 = 21 + 54 \)
\(76 = \frac{ 152 }{ \sqrt{4 } }\)
\(77 = \frac{ 154 }{ 2 }\)
\(78 = ( 15 + 4! ) \cdot 2 \)
\(79 = 21 \cdot 4 - 5 \)
\(80 = ( 12 + 4 ) \cdot 5 \)
\(81 = ( 14 - 5 )^{2 }\)
\(82 = ( 5 - 2 )^{4} + 1 \)
\(83 = \frac{ 5! }{ 2 } - 1 + 4 !\)
\(84 = 12 \cdot 5 + 4 !\)
\(85 = ( 21 - 4 ) \cdot 5 \)
\(86 = ( 1 + 2 )^{4} + 5 \)
\(87 = 41 \cdot 2 + 5 \)
\(88 = ( 45 - 1 ) \cdot 2 \)
\(89 = 21 \cdot 4 + 5 \)
\(90 = ( 2 + 4 ) \cdot 15 \)
\(91 = 45 \cdot 2 + 1 \)
\(92 = ( 41 + 5 ) \cdot 2 \)
\(93 = 41 + 52 \)
\(94 = 214 - 5 !\)
\(95 = ( 21 - \sqrt{4} ) \cdot 5 \)
\(96 = ( 5 - 1 ) \cdot 24 \)
\(97 = 5! - ( 24 - 1 )\)
\(98 = ( 2 + 5 ) \cdot 14 \)
\(99 = 25 \cdot 4 - 1 \)
\(100 = 25 \cdot 1 \cdot 4 \)