Snail Race

Five snails line up on the starting grid -- the starter's pistol goes off... and... after a bit of a slow start, they head towards the finish line. It's a close (but slow) race. Eventually, even the stragglers make it across the line.

Each snail leaves a different type of trail: German Whisper, Renban, Region Sum, Entropic, and Modular. Which snail leaves which trail must be deduced by the solver.

German Whisper: Adjacent digits along the line differ by at least 5.

Renban: The line contains a set of (non-repeating) consecutive digits in any order.

Region Sum: Digits along the line have an equal sum N within each box it passes through; If the line passes through the same box more than once, each individual segment of the path within that box sums to N separately.

Entropic: Every three adjacent digits along the line must contain a low (1-3) digit, a middly (4-6) digit, and a high (7-9) digit.

Modular: Every three adjacent digits along the line must be drawn one from each modulo group: {1,4,7}, {2,5,8}, {3,6,9}.

Digits in cages sum to the clue in the top left corner, if given.