If SS Californian were within 5 miles of Titanic, could she have saved more passengers?

Question

At 8:11 in this Oct 22 1962 BBC interview, Fourth Officer Boxhall of the RMS Titanic contended:

When I heard the crow's nest reported a light on the starboard bow, I went on the bridge right away, found this light with my own glasses. But I wanted the telescope to define what it was, and I realized then that it was two masts headlights of a steamer below the horizon and lights were very close. And I'd went back and told the captain there's a steamer in sight very nearly ahead but slightly on the starboard bow and if she continues in a course she'll pass it close to us down the port side. I asked the captain, "Shall I send up some distress rockets, Sir?" Then we started sending off these distress rockets, the quartermaster and I on the bridge, but I never knew how many I had fired. I knew very well that there was some in the box. A box holds a dozen and when I told the captain I said there are still some in there Sir, but I don't know how many I fired. I didn't see any reply. Some of the passengers that was on the bridge said that they did see a reply. We also called up the ship as she drew closer with a Morse lamp, a very powerful Morse lamp that we had. And eventually this steamer approached and approached until you could see all our lights with a naked eye, and I should say that she must have been within five miles off [emboldening mine]. You could not only see her lights with the naked eye, but you could see the lights in her portholes. So I reckon that she must have been within five miles and then eventually she turned away and showed a stern light. And about that time, the Captain came across the bridge and said, "Mr. Boxhall: you go away in that boat", pointing to the port emergency boat number two, and he said, "hurry up mister" [unaudible], while waiting to lower it. So I said, "You see that white light over there, Sir?", pointing it out to him. He said "yes". I said, "that is the stern light of that ship."

However, Boxhall might've remembered. As the RMS Carpathia never rescued Sixth Officer Moody, Boxhall was wrong to contend at 18:00 of the same interview:

So we Titanic officers, the juniors that was Moody and Moody and Pitman and I we went on watch, as we took soundings because we got fog all the way into New York.

1. I know the SS Californian stopped amid ice, but I don't know if the official inquiries ever assumed that another ship was only 5 miles away. Hence assume that Boxhall is right. In how much time would the Californian have arrived at the Titanic, at reasonable speed in icy waters?

2. What does Boxhall's contention change, if anything? Would more passengers have been saved, or would they have died from the cold by the time the Californian arrived?

Answer 1

The calculation is easy; Britanica article states: "However, the Carpathia was some 58 nautical miles (107 km) away when it received the signal, and it would take more than three hours to reach the Titanic." So if Californian was 5 miles away, it would take at least 15 minutes.

The Carpathia received the distress call at 12:20 am; the Titanic did not founder until 2:18 am, which was two hours after the distress calls were made. "At about 2:00 AM the stern’s propellers were clearly visible above the water, and the only lifeboats that remained on the ship were three collapsible boats. Smith released the crew, saying that “it’s every man for himself.”"

So at about 2:00 am, people began to jump in the water. Only 705 people were rescued by the life boats. "The Carpathia arrived in the area at approximately 3:30 AM, more than an hour after the Titanic sank."

How long does it take for a man to lose consciousness in icy cold water? Hypothermia tables suggest less than 15 minutes. So unless the Californian's arrival was timely, most of those in the water were doomed, and as many could not swim, and were wearing heavy woolens, would have sunk almost immediately.

Note: original testimony from the crew of the Californian put it at least 20 miles away from the closest approach to the Titanic, which was unresponsive to their signals.