All 100 targets have a solution.
\(1 = 75 - 74 \)
\(2 = \sqrt{7 \cdot 7 - 45 }\)
\(3 = \frac{ 5! }{ 47 - 7 }\)
\(4 = 7 \cdot 7 - 45 \)
\(5 = 54 - 7 \cdot 7 \)
\(6 = \frac{ 47 - 5 }{ 7 }\)
\(7 = \sqrt{47 - 5 + 7 }\)
\(8 = \frac{ 47 - 7 }{ 5 }\)
\(9 = 4 + 5 - 7 + 7 \)
\(10 = 57 - 47 \)
\(11 = \frac{ 75 + \sqrt{4} }{ 7 }\)
\(12 = 47 - 5 \cdot 7 \)
\(13 = 7 - ( 5 - 4 ) + 7 \)
\(14 = \sqrt{74 + 7} + 5 \)
\(15 = \sqrt{( 7 - 4 ) \cdot 75 }\)
\(16 = \frac{ 57 + 7 }{ 4 }\)
\(17 = 74 - 57 \)
\(18 = \frac{ 77 - 5 }{ 4 }\)
\(19 = \frac{ 57 }{ 7 - 4 }\)
\(20 = 4 \cdot 5 - 7 + 7 \)
\(21 = \frac{ 5 + 7 }{ 4 } \cdot 7 \)
\(22 = ( 7 - 4 ) \cdot 5 + 7 \)
\(23 = 77 - 54 \)
\(24 = ( 7 \cdot 7 - 45 )!\)
\(25 = \frac{ 75 }{ 7 - 4 }\)
\(26 = 57 - 4! - 7 \)
\(27 = \frac{ \sqrt{4}^{7} + 7 }{ 5 }\)
\(28 = 75 - 47 \)
\(29 = 57 - 4 \cdot 7 \)
\(30 = 4 \cdot 7 - 5 + 7 \)
\(31 = 45 - 7 - 7 \)
\(32 = 77 - 45 \)
\(33 = 4! - 5 + 7 + 7 \)
\(34 = \frac{ 75 - 7 }{ \sqrt{4 } }\)
\(35 = 47 - 5 - 7 \)
\(36 = \frac{ 77 - 5 }{ \sqrt{4 } }\)
\(37 = \frac{ 74 }{ 7 - 5 }\)
\(38 = 45 - \sqrt{7 \cdot 7 }\)
\(39 = 74 - 5 \cdot 7 \)
\(40 = 54 - 7 - 7 \)
\(41 = \frac{ 75 + 7 }{ \sqrt{4 } }\)
\(42 = ( 7 - ( 5 - 4 ) ) \cdot 7 \)
\(43 = 57 - \sqrt{4} \cdot 7 \)
\(44 = 45 - \frac{ 7 }{ 7 }\)
\(45 = 45 - 7 + 7 \)
\(46 = \frac{ 7 }{ 7 } + 45 \)
\(47 = 75 - 4 \cdot 7 \)
\(48 = 57 - \sqrt{4} - 7 \)
\(49 = 47 - 5 + 7 \)
\(50 = ( 7 - 4 + 7 ) \cdot 5 \)
\(51 = 57 - ( 7 - 4 )!\)
\(52 = \sqrt{7 \cdot 7} + 45 \)
\(53 = 54 - \frac{ 7 }{ 7 }\)
\(54 = 54 - 7 + 7 \)
\(55 = \frac{ 7 }{ 7 } + 54 \)
\(56 = ( 5 - 4 + 7 ) \cdot 7 \)
\(57 = 77 - 4 \cdot 5 \)
\(58 = 75 - 4! + 7 \)
\(59 = 45 + 7 + 7 \)
\(60 = 57 - 4 + 7 \)
\(61 = \sqrt{7 \cdot 7} + 54 \)
\(62 = 74 - 5 - 7 \)
\(63 = ( 7 - 4 )! + 57 \)
\(64 = 75 - 4 - 7 \)
\(65 = ( ( 7 - 4 )! + 7 ) \cdot 5 \)
\(66 = 5! - 47 - 7 \)
\(67 = 77 - \sqrt{4} \cdot 5 \)
\(68 = 54 + 7 + 7 \)
\(69 = 75 - ( 7 - 4 )!\)
\(70 = 75 + \sqrt{4} - 7 \)
\(71 = \sqrt{4} \cdot 7 + 57 \)
\(72 = 74 + 5 - 7 \)
\(73 = 7^{7 - 5} + 4 !\)
\(74 = 57 + 4! - 7 \)
\(75 = 5! - ( 7 \cdot 7 - 4 )\)
\(76 = 74 - 5 + 7 \)
\(77 = ( 5 - 4 ) \cdot 77 \)
\(78 = 75 - 4 + 7 \)
\(79 = \frac{ 5! }{ 4 } + 7 \cdot 7 \)
\(80 = 5! - 47 + 7 \)
\(81 = ( 7 - 4 )! + 75 \)
\(82 = \frac{ 574 }{ 7 }\)
\(83 = ( 5 - \sqrt{4} )! + 77 \)
\(84 = 75 + \sqrt{4} + 7 \)
\(85 = 4 \cdot 7 + 57 \)
\(86 = 74 + 5 + 7 \)
\(87 = \sqrt{4} \cdot 5 + 77 \)
\(88 = 57 + 4! + 7 \)
\(89 = \sqrt{4} \cdot 7 + 75 \)
\(90 = ( 4 + 7 + 7 ) \cdot 5 \)
\(91 = ( 4 \cdot 5 - 7 ) \cdot 7 \)
\(92 = 75 + 4! - 7 \)
\(93 = 4! \cdot 7 - 75 \)
\(94 = 7 \cdot 7 + 45 \)
\(95 = \frac{ 7! }{ 7 } - 5^{4 }\)
\(96 = 77 + 4! - 5 \)
\(97 = 4 \cdot 5 + 77 \)
\(98 = ( \sqrt{4} + 5 + 7 ) \cdot 7 \)
\(99 = 5! - 4 \cdot 7 + 7 \)
\(100 = ( 57 - 7 ) \cdot \sqrt{4 }\)