It does indeed look like a custom shop Martin 5-15 Terz guitar.
I have one of the stock models with a solid headstock from the early 2000s. Martin size 5 Terz guitars are designed to be tuned up a minor third (three frets) from standard, giving them a very different voice. Marty Robbins played a Martin 5-18 throughout his career.
I usually keep my 5-15 tuned to Nashville TerzTerz tuning. The top two strings are tuned up three frets from standard, while the bottom four are tuned up three frets plus a full octave from standard. If I then stick a capo on the second fret, I can play along with Ukes without having to transpose!
Here's my 5-15 in action in Nashville Terz tuning.
Scooter