php get array elememnt using $$

Your statement ($$target_arr[5]) is ambiguous. PHP doesn't know what you actually want to say: Do you mean: use $target_arr[5]'s value and prepend the $, to use that as a variable, or do you want to use the value of $target_arr, and get the fifth element of that array?
Obviously it's the latter, but PHP doesn't know that. In order to disambiguate your statement, you have to use curly braces:

${$target_arr}[5];

That'll yield 10. See the manual on variable variables for details

Note:
As people said in comments, and deleted answers: variable variables, like the one you're using is risky business. 9/10 it can, and indeed should be avoided. It makes your code harder to read, more error prone and, in combination with the those two major disadvantages, this is the killer: it makes your code incredibly hard to debug.
If this is just a technical exercise, consider this note a piece of friendly advice. If you've gotten this from some sort of tutorial/blog or other type of online resource: never visit that site again.
If you're actually working on a piece of code, and you've decided to tackle a specific problem using variable vars, then perhaps post your code on code-review, and let me know, I'll have a look and try to offer some constructive criticism to help you on your way, towards a better solution.

Since what you're actually trying to do is copying an array into another variable, then that's quite easy. PHP offers a variety of ways to do that:

Copy by assignment:
PHP copies arrays on assignment, by default, so that means that:

$someArray = range(1,10);//[1,2,3,4,5,6,7,8,9,10]
$foo = $someArray;

Assigns a copy of $someArray to the variable $foo:

echo $foo[0], ' === ', $someArray[0];//echoes 1 === 1
$foo[0] += 123;
echo $foo[0], ' != ', $someArray[0];//echoes 123 != 1

I can change the value of one of the array's elements without that affecting the original array, because it was copied.
There is a risk to this, as you start working with JSON encoded data, chances are that you'll end up with something like:

$obj = json_decode($string);
echo get_class($obj));//echoes stdClass, you have an object

Objects are, by default, passed and assigned by reference, which means that:

$obj = new stdClass;
$obj->some_property = 'foobar';
$foo = $obj;
$foo->some_property .= '2';
echo $obj->some_property;//echoes foobar2!

Change a property through $foo, and the $obj object will change, too. Simply because they both reference exactly the same object.

Slice the array:
A more common way for front-end developers (mainly, I think, stemming from a JS habbit) is to use array_slice, which guarantees to return a copy of the array. with the added perk that you can specify how many of the elements you'll be needing in your copy:

$someArray = range(1,100);//"large" array
$foo = array_slice($someArray, 0);//copy from index 0 to the end
$bar = array_slice($someArray, -10);//copy last 10 elements
$chunk = array_slice($someArray, 20, 4);//start at index 20, copy 4 elements

If you don't want to copy the array, but rather extract a section out of the original you can splice the array (as in split + slice):

$extract = array_splice($someArray, 0, 10);
echo count($someArray);//echoes 90

This removes the first 10 elements from the original array, and assigns them to $extract

Spend some time browsing the countless (well, about a hundred) array functions PHP offers.