The Underwood typewriter was designed and invented by Franz Xaver Wagner. Wagner eventually showed the device to John Thomas Underwood who purchased the rights to manufacture and sell the machine. The first Underwood (No. 1) was introduced to the public between 1896 and 1897, followed by the No. 2, etc. It wasn't until just before 1900 that the Underwood No. 5 was launched. By the No. 5 edition of the typewriter, Wagner had perfected everything that was flawed in the device up to that point. So, the No. 5 was considered the first truly modern typewriter, and was marketed as such.
In fact, the design of the Underwood No. 5 was so popular it became the design standard for all subsequent typewriters, until the 1960s when the IBM Selectric came out. Production of the Underwood 3, 4, and 5 lasted until 1932. Between the three models, the No. 5 was the most popular for several reasons. First, the typebar on the No. 5 gave it speed and accuracy like no other typewriter during that time.
The typebar was a U-shape where the keys rose from the U at the front of the machine to hit the page with precision and force. This U-shape gave the keys a stronger stroke and a deeper indention on the page. All other typebars until that point were "understrokes" instead of a "frontstroke." The understroke machines were called "blind writers" because they typed from the bottom of the platen, not the front. What that meant was the typist had to raise the carriage to see what had been typed. The carriage and keys (frontstroke) on the No. 5 were designed especially for the typists to see the work being typed; a plus in its design and popularity.
Additionally, the key lay-out of the Underwood No. 5 was QWERTY, a standard that has lasted up to today. Look at the keyboard on your own computer. The first few letters on the first line of letter keys reads Q-W-E-R-T-Y and all other letters cascade from this line in such an order that makes finding letters easier as you type. This arrangement of letters was introduced on the Sholes and Gibbon machine of 1874. Several typewriting companies resisted this odd format, but by the late 1800s (1892-94) QWERTY was the standard keyboard layout on most all typewriters.
The last two features of the Underwood No. 5 were the four-bank keyboard with single shift and ribbon inking. A four-bank keyboard with a single shift allowed the typist to type fast. Most keyboards up to that point were "full keyboards" with an individual key for each letter. While some typewriters had three banks of keys along with two-shifts (one for capitals and one for numbers and symbols), but the No. 5 had four-banks and a single shift. The extra bank for numbers and symbols, the single shift for capitals. Like I mentioned earlier, speed was the idea. As for ribbon, other typewriters prior to the Underwood (and later), used ink rollers or ink pads. These required care and frequent replacement. Ribbons, even though the type was not as neat as rollers/pads, needed to be replaced less often and were easier to change.
Besides its popularity in the 1920s, Robert probably chose an Underwood No. 5 based on all the factors above. It is not for certain when he purchased his Underwood No. 5. There is indication from his correspondence that he probably bought one around 1925. Pictured below is an add for the Underwood No. 5 from around 1922-23. Something Robert might have seen in one of the magazines he read.
Underwood No. 5 typewriters are quite common today, even though collectors still collect them. Because of their popularity and the amount that were manufactured between 1900 and 1932, they are not as rare as you might think, making them fairly easy to find and not priced too high. If you ever have the opportunity to type on an Underwood No. 5—I actually have—they are not as easy to use as you might think. The constant pounding down on the large keys can be wearisome. And, after a while your fingers become numb. Which merely means that I'm too spoiled with the ease of use on my computer's keyboard.
If REH did buy his No. 5 in 1925 (and this is likely the case), that would mean the bulk of his work was created on a machine that was built for speed and accuracy. I can imagine him sitting down at his desk pounding out his yarns as he voices them aloud. I can even hear the metallic clicking of the keys as he presses each down; sounding so much like swords clashing.