Steven, that is similar to the 6 strings I am asked to build at times.  The only difference is a single vs. double middle string. 

Bill Berg makes 5-string dulcimers with an interesting set-up...doubled melody strings, single middle, doubled bass tuned an octave apart...makes for a fuller sound, not necessarily louder. I love mine; one of my favorites. I equally love my 3 and 4 string dulcimers. I can only speculate (which I won't do here) why a luthier would insist a beginner buy a 5-string, though. 

The only 5-string dulcimers I make lately with any regularity is my  Extended Range™ dulcimer.  It is basically a combination of a regular & baritone dulcimer with a wider fretboard to accommodate the extra string. It has a very full sound.  You can hear it and read more about it here Extended Range™ Dulcimers  .  Other than a setup like this or some unique tuning, I've never seen the point of a 5-string.

updated by @ron-gibson: 02/25/19 10:34:59AM

I bought a 6 string dulcimer early on thinking that if 4 was good 6 would be better but it was in unmanageable very loud but sounded like a swam of demented bees with the melody almost drowned by the drone. Removed 2 strings and now play the standard dd a d it now sounds beautiful and is a pleasure to play.

The vast majority of the revival and pre-Revival instruments had only 3 courses of single strings -- melody, middle drone and bass.  But pre-Revival luthiers experimented will all sorts of numbers of strings. 

The 4 string, doubled melody course was popularized in the Revival as a way to get more melody volume compared to the mid and bass drones.  

The 5 string, with two doubled course pretty much came from the same era.  They are not common in the dulcimer world today, but not unknown, either.   The idea that all dulcimers must have 5 strings is ludicrous at best.

6 strings -- all courses doubled -- were known a "church"  dulcimers.  The idea being that they had enough volume to be the instrument for services in one-room, backwoods, churches.

Scheitholtz and similar fretted zithers of early America and Europe had as many 16 strings arranged in double, triple and quadruple string courses, as can be seen in the University of Leipzig Instrument collection on-line.

Obviously, all dulcimers do not need to have five strings.  Five strings are not unusual, but dulcimers typically had three strings in the latter half of the 19th century as evidenced by the surviving dulcimers of James Edward "Uncle Ed" Thomas, Charles Napoleon Prichard, and others.  At some point, a four string (double melody) set-up became the standard.  Individual dulcimer makers have experimented with the design of the dulcimer and other variations of the dulcimer (Scheitholt, Epinette des Vosges, Langspil, Langeleik, Hummel, Hungarian Citera, Pennsylvania Dutch Zitters, etc.) exist with more or less than today's standard of three or four strings.  The luthier that stated all dulcimers must have five strings is only stating his personal preferences.  Plenty of evidence exists to prove that dulcimers can and do come with a varying number of strings.  The dulcimer is a folk instrument.  The number of strings is entirely up to each individual to decide for himself or herself.

There are some dulcimer makers whose standard models feature five strings.  I can think of a few.  But there is no standard in which the number of strings defines what is and what is not a dulcimer.  If someone wants a five string dulcimer, by all means purchase one.

By the way I also have a Blue Lion AJ baritone dulcimer.  I ordered it with just three tuners and three strings and Bob and Juanita Baker were very accommodating.  Their dulcimers are in high demand these days, and anyone ordering a Blue Lion can expect a considerable wait.

I have a Blue Lion AJ 5 string. It  came with 5 separate strings [5 tuning machines]. The strings were too close together for my fingers so I removed 2 of them and converted it to a 3 string bass which I play when I'm not using the Folkcraft resonator. I've seen 1-2 with doubled bass and melody strings also. I don't think I would use one although they may be great for noter/drone players, more volume probably.

I just had a couple of friends come over for some look-see at my dulcimers and to discuss playing. She had two dulcimers she had purchased when she first wanted to learn. I won't name the brand but the luthier told her that ALL dulcimers should be five strings. He was adamant about this and when I expressed surprise, the person with her stressed the luthier had a reputation and that he knew what he was talking about.

This led me to wonder. I've been playing for four years. Every friend I know who plays, buys a dulcimer which often comes with four strings, removes the fourth melody string, then goes on playing with three strings.

I have honestly never seen a five string dulcimer and was kind of surprised this luthier stressed this to her... a new player.

Do yall ever see five strings? Why would he have said this?