A while ago I tried and failed to produce a finite structure with this as its congruence lattice by enumerating random structures with a computer program and computing their congruence lattices.
Later, I tried to produce a structure with $N_5$ as its representation lattice, but I learned a few years later that this approach was also incorrect.
What is an example of an algebraic structure with $N_5$ as its congruence lattice?
Here is an ASCII Hasse diagram of $N_5$ for reference:
1
/ \
a c
| |
| b
| /
0
```
