All 100 targets have a solution.
\(1 = 68^{5 - 5 }\)
\(2 = 58 - 56 \)
\(3 = \sqrt{56 + 8} - 5 \)
\(4 = \sqrt{56 - 5 \cdot 8 }\)
\(5 = \frac{ 65 }{ 5 } - 8 \)
\(6 = ( 5 - 5 ) \cdot 8 + 6 \)
\(7 = 65 - 58 \)
\(8 = \frac{ 5! - 56 }{ 8 }\)
\(9 = \frac{ 6! }{ 85 - 5 }\)
\(10 = \frac{ 6 }{ 8 - 5 } \cdot 5 \)
\(11 = \frac{ 85 }{ 5 } - 6 \)
\(12 = \frac{ 56 }{ 8 } + 5 \)
\(13 = 68 - 55 \)
\(14 = \sqrt{86 - 5} + 5 \)
\(15 = \frac{ 85 + 5 }{ 6 }\)
\(16 = 56 - 5 \cdot 8 \)
\(17 = 5 \cdot 6 - 5 - 8 \)
\(18 = \frac{ \frac{ 5! }{ 5 } \cdot 6 }{ 8 }\)
\(19 = 55 - \sqrt{\sqrt{6^{8 }}}\)
\(20 = 85 - 65 \)
\(21 = \frac{ 65 }{ 5 } + 8 \)
\(22 = \frac{ 56 + 5! }{ 8 }\)
\(23 = \frac{ 85 }{ 5 } + 6 \)
\(24 = 5 + 5 + 6 + 8 \)
\(25 = 65 - 5 \cdot 8 \)
\(26 = \frac{ 5! }{ 5 } - 6 + 8 \)
\(27 = 5 \cdot 5 - 6 + 8 \)
\(28 = 58 - 5 \cdot 6 \)
\(29 = 85 - 56 \)
\(30 = 5^{8 - 6} + 5 \)
\(31 = 86 - 55 \)
\(32 = ( 5 + 5 - 6 ) \cdot 8 \)
\(33 = 5 \cdot 6 - 5 + 8 \)
\(34 = \sqrt{5 \cdot 5}! - 86 \)
\(35 = \frac{ 56 \cdot 5 }{ 8 }\)
\(36 = 6^{5 + 5 - 8 }\)
\(37 = ( 8 - 6 )^{5} + 5 \)
\(38 = 58 - \frac{ 5! }{ 6 }\)
\(39 = 5! - 86 + 5 \)
\(40 = \sqrt{56 + 8} \cdot 5 \)
\(41 = 55 - 6 - 8 \)
\(42 = ( 8 - \frac{ 5 }{ 5 } ) \cdot 6 \)
\(43 = 56 - 5 - 8 \)
\(44 = 68 - \frac{ 5! }{ 5 }\)
\(45 = \sqrt{86 - 5} \cdot 5 \)
\(46 = 58 - \sqrt{\frac{ 6! }{ 5 }}\)
\(47 = 58 - 5 - 6 \)
\(48 = ( 5 - 5 + 6 ) \cdot 8 \)
\(49 = \frac{ 5 }{ 5 } + 6 \cdot 8 \)
\(50 = 56 - ( 8 - 5 )!\)
\(51 = 5 \cdot 8 + 5 + 6 \)
\(52 = 65 - 5 - 8 \)
\(53 = 55 + 6 - 8 \)
\(54 = ( \frac{ 5 }{ 5 } + 8 ) \cdot 6 \)
\(55 = 85 - 5 \cdot 6 \)
\(56 = \sqrt{55 - 6} \cdot 8 \)
\(57 = 55 - 6 + 8 \)
\(58 = ( 6 - 5 ) \cdot 58 \)
\(59 = 56 - 5 + 8 \)
\(60 = \sqrt{\frac{ 8! }{ 56 } \cdot 5 }\)
\(61 = 86 - 5 \cdot 5 \)
\(62 = 65 + 5 - 8 \)
\(63 = 5! - 65 + 8 \)
\(64 = ( 5 + 5 - 8 )^{6 }\)
\(65 = 85 - \frac{ 5! }{ 6 }\)
\(66 = ( ( 8 - 5 )! + 5 ) \cdot 6 \)
\(67 = 68 - \frac{ 5 }{ 5 }\)
\(68 = 65 - 5 + 8 \)
\(69 = 55 + 6 + 8 \)
\(70 = 5 \cdot 6 + 5 \cdot 8 \)
\(71 = \frac{ 5! }{ 8 } + 56 \)
\(72 = 5! - 56 + 8 \)
\(73 = \sqrt{5 \cdot 5} + 68 \)
\(74 = 85 - 5 - 6 \)
\(75 = ( 6 + 8 ) \cdot 5 + 5 \)
\(76 = 86 - 5 - 5 \)
\(77 = 5! - ( 6 \cdot 8 - 5 )\)
\(78 = 65 + 5 + 8 \)
\(79 = 85 - \frac{ 6! }{ 5 ! }\)
\(80 = \frac{ 5! }{ 8 } + 65 \)
\(81 = 86 - \sqrt{5 \cdot 5 }\)
\(82 = 5! - 5 \cdot 6 - 8 \)
\(83 = ( 5 + 8 ) \cdot 6 + 5 \)
\(84 = 85 + 5 - 6 \)
\(85 = ( 6 - 5 ) \cdot 85 \)
\(86 = 85 - 5 + 6 \)
\(87 = \frac{ 5 }{ 5 } + 86 \)
\(88 = 5 \cdot 6 + 58 \)
\(89 = \frac{ 6! }{ 8 } - \frac{ 5 }{ 5 }\)
\(90 = ( 8 - 5 ) \cdot 5 \cdot 6 \)
\(91 = \sqrt{5 \cdot 5} + 86 \)
\(92 = \frac{ 5! }{ 5 } + 68 \)
\(93 = \frac{ 558 }{ 6 }\)
\(94 = \sqrt{\sqrt{( 5 + 5 )^{8}}} - 6 \)
\(95 = ( 5 + 6 + 8 ) \cdot 5 \)
\(96 = 5 \cdot 8 + 56 \)
\(97 = \sqrt{\frac{ 6! }{ 5 }} + 85 \)
\(98 = 5! - 5 \cdot 6 + 8 \)
\(99 = 5! - \frac{ 5! }{ 8 } - 6 \)
\(100 = ( 5 + 5 )^{8 - 6 }\)