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