Cat5 socket wiring issues

TL;DR: Yes, you can just follow the colours on the back of the sockets.

Expanded answer: Ethernet uses four pairs of wires with differential signaling. In the cable, the two wires in a pair are twisted around each other, following the colors: green and green-white, blue and blue-white, etc. The pairs have a slightly different rate of number of twists per length. That reduces crosstalk between pairs, so it's important to get the pairs right.

There are actually two ways to distribute the pairs, 568A and 568B. For a cross-over patch cable, you'd crimp one end according to 568A, and the other according to 568B. But today's hardware can automatically adjust to cross-over or straight-through connections, so getting this right is only important if you are using really old hardware.

In theory, a cross-over connection could also be made between sockets (not following the colors on one end), but you can always do the crossing over in a patch cable, if really necessary. So just following the colours in the sockets is fine.

Additional info, because this regularly trips up people: There are two kinds of Cat5 wires, a solid-core "installation" variant and a stranded "patch" variant. The solid-core "installation" variant is one you should run inside the walls and connect with the sockets in your picture. If you try to connect the stranded "patch" variant to those sockets, the connection will be bad.

Because the this variant is a bit stiffer, be careful when bending it, and don't try to put it around sharp corners.

Vice versa, most RJ45 plugs are for the stranded "patch" variant. If you try to crimp the solid-core "installation" variant, the connection is not firm and will come loose over time (or immediately, in some cases). There are special RJ45 plugs together with special crimp tools that work for the solid-core variant. So in a pinch, if you really must, you can put an RJ45 plug of those. But usually it's better to just put in a socket in this place, and use a patch cable to get a plug.

In any case, make sure to buy and use the correct type of cable with the sockets and RJ45 plugs you have.