Question: Which battle took place first Battle of Cold Harbor or Battle of Iwo Jima ?

Context paragraphs:
USS Dewey (DD-349): The first USS "Dewey" (DD-349) was a "Farragut"-class destroyer of the United States Navy, launched in 1934 and named for Admiral George Dewey.  "Dewey" served in the Pacific through World War II.  After escaping damage during the attack on Pearl Harbor, "Dewey" screened the aircraft carrier USS "Lexington" until the carrier was lost in the battle of the Coral Sea; then screened USS "Saratoga" through the invasion of Guadalcanal and the battle of the Eastern Solomons.  Following overhaul in San Francisco, "Dewey" spent 1943 in Alaskan waters supporting the invasions of Attu and Kiska.  "Dewey" spent 1944 supporting raids in the Marshalls, Carolines, and Marianas, including screening carriers during the battle of the Philippine Sea.  After being damaged by Typhoon Cobra during the recapture of the Philippines, "Dewey" supported the invasion of Iwo Jima and spent the remainder of the war screening replenishment oilers.

Iwo Jima-class amphibious assault ship: The "Iwo Jima"-class amphibious assault ships of the United States Navy were the first amphibious assault ships designed and built as dedicated helicopter carriers, capable of operating up to 20 helicopters to carry up to 1,800 marines ashore.  They were named for battles featuring the United States Marine Corps, starting with the Battle of Iwo Jima.  The first ship of the class was commissioned in 1961, and the last was decommissioned in 2002.  Because these ships bore the hull classification of LPH they have often been referred to as "Landing Platform, Helicopter".

Battle of Cold Harbor: The Battle of Cold Harbor was fought from May 31 to June 12, 1864, with the most significant fighting occurring on June 3.  It was one of the final battles of Union Lt. Gen. Ulysses S. Grant's Overland Campaign during the American Civil War, and is remembered as one of American history's bloodiest, most lopsided battles.  Thousands of Union soldiers were killed or wounded in a hopeless frontal assault against the fortified positions of Confederate Gen. Robert E. Lee's army.

USS Iwo Jima (LPH-2): USS "Iwo Jima" (LPH-2) was the lead ship of her class and type—the first ship to be designed and built from the keel up as an amphibious assault ship.  She carried helicopters and a detachment of embarked Marines for use in the Navy's "vertical envelopment" concept of amphibious operations.  "Iwo Jima" was the second of three ships of the United States Navy to be named for the Battle of Iwo Jima, although the first to be completed and see service (the first was cancelled during construction).

Battle of Ticinus: The Battle of Ticinus was a battle of the Second Punic War fought between the Carthaginian forces of Hannibal and the Romans under Publius Cornelius Scipio in November 218 BC.  The battle took place in the flat country of Pavia county on the right bank of the Ticino River, not far north from its confluence (from the north) with the Po River.  The battle is named from the river, not the nearby contemporaneous settlement of Ticinum (today's Pavia).  Although the precise location is not known, it is generally accepted that a settlement known today as Vigevano is mentioned in Livy's text and that Scipio's camp was to the south at Gambolo, whose coordinates are given on the map.  The conflict would have been west of there.  It was the first battle of the war against the Romans that was fought on Italian soil and the first battle of the war to employ legion-sized forces.  Its loss by the Romans, and the temporary disablement of Scipio's command, set the stage for the Roman disaster at the Battle of Trebbia in December.

5th Marine Division (United States): The 5th Marine Division was a United States Marine Corps infantry division which was activated on 11 November 1943 (officially activated on 21 January 1944) at Camp Pendleton, California during World War II.  The 5th Division saw its first combat action during the Battle of Iwo Jima in 1945 where it sustained the highest number of casualties of the three Marine divisions of the V Amphibious Corps (invasion force).  The 5th Division was to be part of the planned invasion of the Japan homeland before Japan surrendered.  Assault troops of the 5th Division were included in the Presidential Unit Citation awarded to the V Amphibious Corps for extraordinary heroism on Iwo Jima from 19 to 28 February 1945.  The 5th Division was deactivated on 5 February 1946.

Battle of Gaines's Mill: The Battle of Gaines's Mill, sometimes known as the First Battle of Cold Harbor or the Battle of Chickahominy River, took place on June 27, 1862, in Hanover County, Virginia, as the third of the Seven Days Battles (Peninsula Campaign) of the American Civil War.  Following the inconclusive Battle of Beaver Dam Creek (Mechanicsville) the previous day, Confederate General Robert E. Lee renewed his attacks against the right flank of the Union Army, relatively isolated on the northern side of the Chickahominy River.  There, Brig. Gen. Fitz John Porter's V Corps had established a strong defensive line behind Boatswain's Swamp.  Lee's force was destined to launch the largest Confederate attack of the war, about 57,000 men in six divisions.  Porter's reinforced V Corps held fast for the afternoon as the Confederates attacked in a disjointed manner, first with the division of Maj. Gen. A.P. Hill, then Maj. Gen. Richard S. Ewell, suffering heavy casualties.  The arrival of Maj. Gen. Stonewall Jackson's command was delayed, preventing the full concentration of Confederate force before Porter received some reinforcements from the VI Corps.

To the Shores of Iwo Jima: To the Shores of Iwo Jima is a 1945 Kodachrome color short war film produced by the United States Navy and United States Marine Corps.  It documents the Battle of Iwo Jima, and was the first time that American audiences saw in color the footage of the famous flag raising on Iwo Jima.

Battle of Iwo Jima: The Battle of Iwo Jima (19 February – 26 March 1945) was a major battle in which the United States Marine Corps landed on and eventually captured the island of Iwo Jima from the Imperial Japanese Army during World War II.  The American invasion, designated Operation Detachment, had the goal of capturing the entire island, including the three Japanese-controlled airfields (including the South Field and the Central Field), to provide a staging area for attacks on the Japanese main islands.  This five-week battle comprised some of the fiercest and bloodiest fighting of the Pacific War of World War II.

Battle of Savo Island: The Battle of Savo Island, also known as the First Battle of Savo Island and, in Japanese sources, as the First Battle of the Solomon Sea (第一次ソロモン海戦 , Dai-ichi-ji Soromon Kaisen ) , and colloquially among Allied Guadalcanal veterans as The Battle of the Five Sitting Ducks, was a naval battle of the Pacific Campaign of World War II between the Imperial Japanese Navy and Allied naval forces.  The battle took place on August 8–9, 1942 and was the first major naval engagement of the Guadalcanal campaign, and the first of several naval battles in the straits later named Ironbottom Sound, near the island of Guadalcanal.

Supporting paragraphs: Battle of Cold Harbor Battle of Iwo Jima
Answer: Battle of Cold Harbor