Yes, you can hike this!
First, the USFS is a little backward and short in their trail direction and data. This is largely because trail #5006 is really an old logging road turned into an ATV track that can be hiked, not a built foot path. In reality, 5006 only runs about 2 miles, but if you came to hike you'll actually want to do that, and from a parking area. Also, you'll probably want a destination that is not simply a road junction. Perhaps the Benson Ridge/ Sacramento Mountain Highpoint? As all of the trails in the Benson Ridge area seem to be open to ATV's, and are basically ATV trails, you may want to avoid this area from May to September, when it is overflowing with Texans riding around on their loud, smelly, 2-stroke engine, glorified lawnmowers. I mean ATVs. Serious, I visited and left in disgust in 2003, due to the huge numbers of ATV use. Weekend use is probably outrageous.
Most of this hike is in fairly dense Fir forest, both Douglas and White, with some Aspen throughout, and a little Ponderosa Pine near the lower areas and even some Englemann Spruce near the top. It's shady, cool, and probably moist most of the time. I found light snow patches in mid-April after a dry winter. I also chanced to do this on a very cold, moist and overcast day. In shorts! It was wishful thinking. Anyway, plan for temps 20 to 30 degrees cooler than Alamogordo, and likely rain in monsoon season. This would make a decent snowshoe area in winter after a big storm.
If you are like me, hikes go up, not down, so you will begin at the Bluff Springs Trailhead, picnic area, and scenic waterfall view point. On the north side of the Rio Penasco Road is an old style wire cattle fence. The hike begins by going through that and starting up the road. This is either 5597, or 5597B. I forget, but either way, hike up hill on the path about 1/4 a mile and take the left fork onto 5597, which is signed with a small carbonite sign as "5597". Proceed on this gentle up hill path to the official trailhead, which is marked with a nice obvious sign. This point begins your hike on road, path, or trail #5006.
Trail 5006 ascends at a gentle pace for a little over 2 miles. Slightly beyond the half way point, you will come to an intersection with #5005A. Ignore this and keep on the main stem and follow 5006. The next intersection is with 5007C, which may not be obvious but it is slightly open in this area. Keep on 5006 about another 3/4 of a mile and find the upper trailhead. This is marked with a nice sign as well and you can't miss it. This is where 5006 meets 5007, and it hardly seems like a destination. Continue on 5007 to the Benson Ridge Road, AKA FR 223. As you approach 223, notice the higher terrain above the road to the north of the intersection and between the two sections of 223, which forms a "V" in this area as it wraps around you destination. Hike up this hill, cross a very slight saddle and ascend to the recently thinned, but still dense with aspen and white fir highpoint at 9695'.
On the "summit", there is a red can with a register in it. It was obvious the day I hiked this. Views are lacking, but you can see Sierra Blanca though the trees, as well as the Organ Mountains in a few locations. This more or less boring hill needs a fire tower, or something. Return the way you hiked up.
WARNING! Hiking and outdoor related sports can be dangerous. Be responsible and prepare for the trip. Study the area you are entering and plan accordingly. Dress for the current and unexpected weather changes. Take plenty of water. Never go alone. Make an itinerary with your plan(s), route(s), destination(s) and expected return time. Give your itinerary to trusted family and/or friends.