I looked at other people's answers for the first four grids, and got the solutions from those. However, here's what I think the fifth grid is (minor spoilers for the other four grids):
It has a unique solution:
As in many grid-deduction puzzles (and for that matter well-posed logical deduction puzzles of all kinds), you can usually deduce the solution by pure logic from the given initial conditions. The fact that you can deduce it shows that it's unique, otherwise you'd find more than one possibility.
If such a puzzle doesn't have a unique solution, then it's ...
In this answer, I use "RxCy" for the cell in the x-th row (from the top) and the y-th column (from the left).
Following directly from that,
Now that the top left is resolved,
Now we move to the top right:
Finally, we've reached the bottom!
The answer is
(This was very well done, although it's a shame that the methods I used were taught to me by my Slitherlink Master - i.e, they were not new to me)
Method of solution:
Now, fill in some obvious stuff and do another chain, one below this one (a blend of twos chained diagonally, with 0 entrances on one end - if we have ...
My solution is:
First step: start from mid of top row
Last step: Combine the ends.
One of the solution on my page: that explains possibilities for top 2 and bottom 3's, when i was stuck on second 2:
Here are three sites where you can find very difficult puzzles:
If you want to start with the most difficult, try an "Unlimited" at the first site.