In the Battle of the Department of Mysteries, there were more than 12 Death Eaters, why were only 5 Order members (Remus Lupin, Sirius Black, Alastor Moody, Kingsley Shacklebolt and Nymphadora Tonks) sent to rescue Harry Potter, Luna Lovegood, Ron Weasley, Neville Longbottom, Hermione Granger, and Ginny Weasley?

Where were the other Order members? Surely there were more than 5 guys in the Order, right?

There were approximately twenty members in the Order, as per Mr. Weasley's comment in the beginning of Deathly Hallows:

"And as there are around twenty of us, that greatly dilutes the power
of the Fidelius Charm.

However, not every member is always available at a moment's notice. In this particular case, Dumbledore tells Harry when they get back to his office that the ones who came were the ones who happened to be around at the time:

“When, however, you did not return from your trip into the forest with
Dolores Umbridge, Professor Snape grew worried that you still believed
Sirius to be a captive of Lord Voldemort’s. He alerted certain Order
members at once.”

Dumbledore heaved a great sigh and then said, “Alastor Moody,
Nymphadora Tonks, Kingsley Shacklebolt, and Remus Lupin were at
headquarters when he made contact. All agreed to go to your aid at
once. Professor Snape requested that Sirius remain behind, as he
needed somebody to remain at headquarters to tell me what had
happened, for I was due there at any moment. In the meantime he,
Professor Snape, intended to search the forest for you.

Additionally, we don't really know that much about the other Order members. Some of them might have been more peripheral members, who were not so involved in day-to-day operations. Also, not everyone is cut out for such a mission. The ones that did go are people that we know are capable of handling an altercation with Death Eaters. It is possible that certain other members would not have gone even if they had been available. For example, Mrs. Figg would not be of much use in a battle, and Mundungus Fletcher would probably not want to risk the danger unless he was forced into it.

Lastly, the Order didn't know know many Death Eaters were at the Ministry. It is possible that had they known there would be so many Death Eaters they would have attempted to gather reinforcements.

Only five members of the Order were at the headquarters then.

When Snape contacted the Order headquarters, there were five members present. Sirius was also there, but he wasn’t actually supposed to go - he was supposed to stay at headquarters.

“When, however, you did not return from your trip into the Forest with Dolores Umbridge, Professor Snape grew worried that you still believed Sirius to be a captive of Lord Voldemort’s. He alerted certain Order members at once.’

Dumbledore heaved a great sigh and continued, ‘Alastor Moody, Nymphadora Tonks, Kingsley Shacklebolt and Remus Lupin were at Headquarters when he made contact. All agreed to go to your aid at once. Professor Snape requested that Sirius remain behind, as he needed somebody to remain at Headquarters to tell me what had happened, for I was due there at any moment.”
_{^{- Harry Potter and the Order of the Phoenix, Chapter 37 (The Lost Prophecy)}}

All five of the members who were at headquarters at the time showed up at the Ministry.

Not all of the members were fighters.

All of the members of the Order contributed in some way, but not all of them were fighters. Arabella Figgs, for example, was a Squib and could not do magic. And Mr. and Mrs. Weasley, although they could definitely duel, as we saw in the Battle of Hogwarts, helped in different ways.

Some were not available at the time.

Many of the Order members had full-time jobs, and a few lived farther away. Although many of those people could have Apparated, it was easier to just whip up a quick team of fighters already at Grimmauld Place and call on backup (Dumbledore) if needed.