All 100 targets have a solution.
\(1 = 24^{5 - 5 }\)
\(2 = 54 - 52 \)
\(3 = \sqrt{\frac{ 45 }{ \sqrt{25 } }}\)
\(4 = 5 - ( \sqrt{25} - 4 )\)
\(5 = \frac{ 25 - 5 }{ 4 }\)
\(6 = \sqrt{25} - 4 + 5 \)
\(7 = 52 - 45 \)
\(8 = \frac{ 52 }{ 4 } - 5 \)
\(9 = \frac{ 45 }{ \sqrt{25 } }\)
\(10 = \frac{ 5! }{ 24 } + 5 \)
\(11 = \frac{ 45 }{ 5 } + 2 \)
\(12 = 5! - 54 \cdot 2 \)
\(13 = 55 - 42 \)
\(14 = 24 - 5 - 5 \)
\(15 = \frac{ 45 }{ 5 - 2 }\)
\(16 = 25 - 4 - 5 \)
\(17 = 42 - 5 \cdot 5 \)
\(18 = \frac{ 45 \cdot 2 }{ 5 }\)
\(19 = 24 - \sqrt{5 \cdot 5 }\)
\(20 = 45 - 25 \)
\(21 = \sqrt{25} \cdot 5 - 4 \)
\(22 = \frac{ 54 }{ 2 } - 5 \)
\(23 = \sqrt{524 + 5 }\)
\(24 = 24 - 5 + 5 \)
\(25 = \frac{ 5 }{ 5 } + 24 \)
\(26 = 25 - 4 + 5 \)
\(27 = 52 - 5^{\sqrt{4 }}\)
\(28 = 25 - \sqrt{4} + 5 \)
\(29 = 54 - 25 \)
\(30 = \frac{ ( \frac{ 25 }{ 5 } )! }{ 4 }\)
\(31 = 55 - 24 \)
\(32 = 42 - 5 - 5 \)
\(33 = 52 - 4! + 5 \)
\(34 = 24 + 5 + 5 \)
\(35 = \sqrt{245 \cdot 5 }\)
\(36 = ( 5 - 4 + 5 )^{2 }\)
\(37 = 42 - \sqrt{5 \cdot 5 }\)
\(38 = 45 - 2 - 5 \)
\(39 = 55 - 2^{4 }\)
\(40 = 45 - \sqrt{25 }\)
\(41 = 42 - \frac{ 5 }{ 5 }\)
\(42 = 42 - 5 + 5 \)
\(43 = \frac{ 5 }{ 5 } + 42 \)
\(44 = 54 - 2 \cdot 5 \)
\(45 = 4 \cdot 5 + 25 \)
\(46 = 2 \cdot 5 \cdot 5 - 4 \)
\(47 = 54 - 2 - 5 \)
\(48 = 45 - 2 + 5 \)
\(49 = \frac{ 245 }{ 5 }\)
\(50 = \sqrt{25} + 45 \)
\(51 = 52 + 4 - 5 \)
\(52 = 42 + 5 + 5 \)
\(53 = 52 - 4 + 5 \)
\(54 = 25 + 4! + 5 \)
\(55 = 2 \cdot 5 + 45 \)
\(56 = \frac{ 2 }{ \sqrt{4} } + 55 \)
\(57 = 54 - 2 + 5 \)
\(58 = ( 5 \cdot 5 + 4 ) \cdot 2 \)
\(59 = \sqrt{25} + 54 \)
\(60 = ( 25 + 5 ) \cdot \sqrt{4 }\)
\(61 = 52 + 4 + 5 \)
\(62 = \sqrt{4} \cdot 5 + 52 \)
\(63 = 2 \cdot 4 + 55 \)
\(64 = 2 \cdot 5 + 54 \)
\(65 = \frac{ 52 }{ 4 } \cdot 5 \)
\(66 = \sqrt{25}! - 54 \)
\(67 = 5 \cdot 5 + 42 \)
\(68 = 4! \cdot 5 - 52 \)
\(69 = 4^{5 - 2} + 5 \)
\(70 = 25 + 45 \)
\(71 = 2^{4} + 55 \)
\(72 = 4 \cdot 5 + 52 \)
\(73 = 5! - ( 42 + 5 )\)
\(74 = ( 2^{5} + 5 ) \cdot \sqrt{4 }\)
\(75 = \sqrt{25}! - 45 \)
\(76 = ( 5 - 2 )^{4} - 5 \)
\(77 = 2^{5} + 45 \)
\(78 = \sqrt{5 \cdot 5}! - 42 \)
\(79 = 24 + 55 \)
\(80 = ( 25 - 5 ) \cdot 4 \)
\(81 = ( \frac{ 45 }{ 5 } )^{2 }\)
\(82 = \frac{ 5! }{ 4 } + 52 \)
\(83 = 5! - ( 42 - 5 )\)
\(84 = \sqrt{4}^{5} + 52 \)
\(85 = \frac{ 425 }{ 5 }\)
\(86 = 2^{5} + 54 \)
\(87 = \frac{ 54 + 5! }{ 2 }\)
\(88 = 52 \cdot 4 - 5 !\)
\(89 = 5! - ( 2 + 4! + 5 )\)
\(90 = 42 \cdot 5 - 5 !\)
\(91 = 5! - ( 24 + 5 )\)
\(92 = ( 5 \cdot 5 - 2 ) \cdot 4 \)
\(93 = 5! - \frac{ 54 }{ 2 }\)
\(94 = ( 52 - 5 ) \cdot \sqrt{4 }\)
\(95 = ( 24 - 5 ) \cdot 5 \)
\(96 = ( 5 + 5 )^{2} - 4 \)
\(97 = 42 + 55 \)
\(98 = ( 54 - 5 ) \cdot 2 \)
\(99 = 5! - ( 25 - 4 )\)
\(100 = ( 45 + 5 ) \cdot 2 \)