All 100 targets have a solution.
\(1 = \frac{ 13 - 5 }{ 8 }\)
\(2 = \frac{ 5! }{ 8 } - 13 \)
\(3 = 8 - \frac{ 15 }{ 3 }\)
\(4 = 15 - 3 - 8 \)
\(5 = \frac{ 35 }{ 8 - 1 }\)
\(6 = \frac{ 51 - 3 }{ 8 }\)
\(7 = 13 - ( 8 - 5 )!\)
\(8 = \sqrt{( 13 - 5 ) \cdot 8 }\)
\(9 = 3 \cdot 8 - 15 \)
\(10 = 13 + 5 - 8 \)
\(11 = \frac{ 18 }{ 3 } + 5 \)
\(12 = \sqrt{( 13 + 5 ) \cdot 8 }\)
\(13 = 51 - 38 \)
\(14 = \sqrt{31 + 5} + 8 \)
\(15 = \frac{ ( \frac{ 15 }{ 3 } )! }{ 8 }\)
\(16 = 13 - 5 + 8 \)
\(17 = 35 - 18 \)
\(18 = 138 - 5 !\)
\(19 = \frac{ 58 - 1 }{ 3 }\)
\(20 = 15 - 3 + 8 \)
\(21 = ( 15 - 8 ) \cdot 3 \)
\(22 = \frac{ 81 }{ 3 } - 5 \)
\(23 = 38 - 15 \)
\(24 = \frac{ 5! }{ 13 - 8 }\)
\(25 = ( 13 - 8 ) \cdot 5 \)
\(26 = 35 - \sqrt{81 }\)
\(27 = 58 - 31 \)
\(28 = 81 - 53 \)
\(29 = \frac{ 58 }{ 3 - 1 }\)
\(30 = \frac{ 18 }{ 3 } \cdot 5 \)
\(31 = \frac{ 5! }{ 3 } - \sqrt{81 }\)
\(32 = 83 - 51 \)
\(33 = 3 \cdot 5 + 18 \)
\(34 = 31 - 5 + 8 \)
\(35 = 53 - 18 \)
\(36 = ( 5 - 3 ) \cdot 18 \)
\(37 = 15 \cdot 3 - 8 \)
\(38 = 1^{5} \cdot 38 \)
\(39 = ( 8 - 5 ) \cdot 13 \)
\(40 = \frac{ 15 }{ 3 } \cdot 8 \)
\(41 = 81 - \frac{ 5! }{ 3 }\)
\(42 = 35 - 1 + 8 \)
\(43 = 35 \cdot 1 + 8 \)
\(44 = 35 + \sqrt{81 }\)
\(45 = 58 - 13 \)
\(46 = 81 - 35 \)
\(47 = 53 - \sqrt{\sqrt{81 }}!\)
\(48 = 3! \cdot 5 + 18 \)
\(49 = 18 \cdot 3 - 5 \)
\(50 = 53 - \sqrt{\sqrt{81 }}\)
\(51 = 58 - 1 - 3 !\)
\(52 = 53 - 1^{8 }\)
\(53 = 15 + 38 \)
\(54 = 85 - 31 \)
\(55 = 58 \cdot 1 - 3 \)
\(56 = 51 - 3 + 8 \)
\(57 = 13 \cdot 5 - 8 \)
\(58 = 1^{3} \cdot 58 \)
\(59 = 18 \cdot 3 + 5 \)
\(60 = 53 - 1 + 8 \)
\(61 = 53 \cdot 1 + 8 \)
\(62 = 53 + \sqrt{81 }\)
\(63 = 183 - 5 !\)
\(64 = ( 13 - 5 ) \cdot 8 \)
\(65 = 51 + 3! + 8 \)
\(66 = 81 - 3 \cdot 5 \)
\(67 = \frac{ 81 + 5! }{ 3 }\)
\(68 = 83 - 15 \)
\(69 = ( 15 + 8 ) \cdot 3 \)
\(70 = 81 - 3! - 5 \)
\(71 = 13 + 58 \)
\(72 = 85 - 13 \)
\(73 = 13 \cdot 5 + 8 \)
\(74 = \sqrt{\sqrt{5^{8}}} \cdot 3 - 1 \)
\(75 = ( 8 - 3 ) \cdot 15 \)
\(76 = \sqrt{5 - 1} \cdot 38 \)
\(77 = 83 - 1 - 5 \)
\(78 = 83 \cdot 1 - 5 \)
\(79 = 81 + 3 - 5 \)
\(80 = 81 - 3! + 5 \)
\(81 = 85 - 1 - 3 \)
\(82 = 83 - 1^{5 }\)
\(83 = 81 - 3 + 5 \)
\(84 = 1^{5} + 83 \)
\(85 = 1^{3} \cdot 85 \)
\(86 = 1^{3} + 85 \)
\(87 = 18 \cdot 5 - 3 \)
\(88 = 83 \cdot 1 + 5 \)
\(89 = 31 + 58 \)
\(90 = 85 - 1 + 3 !\)
\(91 = 85 \cdot 1 + 3 !\)
\(92 = 81 + 3! + 5 \)
\(93 = 18 \cdot 5 + 3 \)
\(94 = \sqrt{1 + 5!} + 83 \)
\(95 = 815 - 3 !!\)
\(96 = ( 15 - 3 ) \cdot 8 \)
\(97 = 5! - 31 + 8 \)
\(98 = 13 + 85 \)
\(99 = 13 \cdot 8 - 5 \)
\(100 = \sqrt{\sqrt{( ( 3 - 1 ) \cdot 5 )^{8 }}}\)