I conducted tests 1 and 2 on the ground and then all 3 tests 30 blocks up in the air just to make sure there were no entities around me.

Test 1

/execute unless score @e[distance=..5,limit=1] s1 = @s s1

Test passed

Test 2

/execute unless score @e[tag=place_holder,distance=..5,limit=1] s1 = @s s1

No entity was found

Test 3

/execute unless entity @e[tag=place_holder,distance=..5,limit=1]

Test passed

Expected results:
Test 1: Results are as expected, there is no entity in range so it should pass.
Test 2: If there is no entity then there can be no score, test should pass.
Test 3: Results are as expected, there is no entity in range so it should pass.