Write a number in every cell. Equal numbers that are neighbours either horizontally or vertically automatically belong to the same group. Every group needs to consist of exactly as many cells as this number indicates. This means you can not have two groups with the same number sharing a border.

It is most convenient to start with the number 6; since there are at most five other cells that can become connected to it, they must all be a 6.

The 3 in the third column can only extend to the left and consequently meets yet another 3 above it, which completes this group.

The 2 on the top row can now only extend to the left, after which just five cells remain which all need to have a 5 written in them.

.