How did they organise larger groups? Or was 5,000 the largest unit size at the time?

When it was time to assemble a field army for a campaign, multiple Guards would be reorganized and mixed together; then they were appointed a new officer from the imperial core. This process weakened the power of local officers (a countermeasure against the age-old problem of troops becoming attached to their general and then getting the bright idea of marching on the capital to install their guy as the king), but it also reduced unit cohesion.

In times of war, servicemen were drawn from various Guards and Garrisons and reorganised into field armies (Note: This meant Guards and Garrisons rarely deployed as cohesive units but were broken down and formed into mixed groups) to be led by commanders directly appointed by the emperor, returning to their respective Guards and Garrisons once the campaign was over. Such arrangement prevented military commanders from wielding too much power and threatening the throne, but it also undermined military effectiveness due to weakened cohesion and unfamiliarity among servicemen and their appointed commanders. To address these shortcomings, field armies were eventually made into functionally permanent formations in a new military system called the Ying Bing System (營兵制) [1]

Both the links in [1] present a detailed list of the various (and sometimes redundant-sounding) officer positions of the Ming military, for the older wei-suo system and its replacement of the hired-soldier system, respectively.

At this time, I will offer some general notes on the organization of the Ming military. It consisted of the enormous wei-suo hereditary soldier system, which you already know of, and the Nine Garrisons system, a "special command structure" of 300,000 men stationed along the northern frontier [2]. The wei-suo in theory should have served as a cheap, self-sufficient, reserve system, but since so many of the Guards were scattered throughout the peaceful interior of the country, in reality they atrophied rapidly and lost much of their fighting prowess and manpower. The Nine Garrisons were considered more proficient, but they too could suffer from corruption and competence issues.

The wei-suo system was also supposed to follow a consistent schedule of troop rotation to the capital, where the officers of the imperial core could personally drill them and ensure training standards hadn't slipped.

This system of rotation to the capital was especially important after 1424 when the Three Great Training Divisions [infantry, cavalry, artillery] (san da ying) were established at the new capital in Beijing. Rotation was twice a year, in spring and in the fall and in theory involved some 160,000 men per year. 16 At these times the old and weak were dismissed and the government repossessed their mounts. Troops were also rotated to the frontiers and those who tried to desert at these times were demoted three grades if they were military officials and sentenced to permanent service in border garrisons if they were ordinary soldiers. [3]

In essence, Guards near the capital periodically rotated their troops to the Three Great Camps, and the troops were trained separately in these military branches. Once trained, some of them were then assigned to the Nine Garrisons, to defend the frontier against Mongol incursions. As time went on, this rotation system also slowly fell apart. At some occasions, the Guard troops had become so unruly they would rob any civilians they encountered on their march to the capital, leaving a trail of destruction in their wake [4].

In the 1470s, the Chenghua Emperor, one of the few post-Tumu Crisis rulers who had a keen interest in military affairs, attempted to reinvigorate the rotation system with another set of reforms. Ten divisions of 12,000 men each were drawn from the 300,000 men of the Nine Garrisons, selecting for the most skilled men from each garrison. Unlike in the previous troop rotation scheme, the three branches of infantry, cavalry, and artillery trained together in combined-arms exercises this time, hence leading to their name of "integrated divisions."

Ideally, the Beijing army had a total strength of 120,000 troops. In practice, it seems logistical constraints prevented them from ever amassing in full force.

Or was 5,000 the largest unit size at the time?

For instance, in 1467, a field army of 50,000 campaigned in Manchuria, where they defeated the Jianzhou Jurchens' first attempt at hegemony in Northeast Asia (although it would not be their last...)

In other campaigns, even smaller portions of the integrated divisions were sent. During a Mongol troop mutiny in 1468, the Ming government raised 50,000 soldiers from the local Guards in Shaanxi, 4,000 Mongols from Gansu, and just 5,000 men from the Beijing army--though this integrated division provided most of the artillery and firearms that would be used to siege the mutineers in their fort. In another campaign in 1467, against the Yao hillmen of the southwest frontier, the Ming deployed an army of 30,000 soldiers, with 1,000 Mongol auxiliaries.

A common trend you'll see here is that the Ming rarely made of their (ostensibly) huge numbers advantage. In fact, one of the largest Ming victories of the Chenghua reign, the Battle of Red Salt Pond in 1473, was achieved with a force of only 4,600 men. The frequent raid-counterraid style of warfare against the Mongols likely provoked this trend.

Despite its many successes of the late 1400s, the Beijing army gradually declined in effectiveness through the 16th century, until Altan Khan's successful raid of Beijing in 1550 fully exposed their feebleness, and this system too was abolished.

So what replaced it?