You can tattoo them and tag them their first day. I prefer to tag them in the first 24 hours and tattoo them at weaning. By weaning the ear is bigger and it is easier to get the whole tattoo in the white skin so it will show up well. My angus cattle have skin that turns blacker as you move toward the tip of the ear and some of the skin that is white (pink) at birth seems to get more pigment as they get older.
Our association requires that you tatoo calf at birth, this is really not neccessary and can cause undo stess to both calf and dam, I prefew to tattoo at weaning, and if there are some to cull at that time, I have not waisted time and effort. 5 weeks is old enough, and I would have already tagged them in my own herd by the time theye are a week to two weeks of age with their herd ID number, remember when tagging females that are young, you will be Bangs vaccinating them, we do not tag in the ID tatoo ear, but we place the tag deep enough in the right ear so that the tag does not have to be reoved for Bangs Tattoo placement, we use the Z-tags so they are not reusable, but they also don't fall out.
Also, wipe the ear with a clean dry rag, do not use alcohol, it works agains the ink and will cause your tattoo to be light or not to take at all, we soak or tattoo gun and digits in Nolvasan Soln. and dry in on a clean towel, we have not had any trouble with this causing the tattoo not to take, we also use the roll on tattoo ink, there are two methods, ink the ear, then tattoo, tattoo and then ink, the latter is the method I use, but I also wash off the ink bottle when through for storage, and to prevent filth from being left on the inking surface. Tatto ink stains so wear gloves or wash soon after with soapy warm water, it will come right out, some prefer to use the tattoo paste, then an old soft toooth brush to work the ink into the fresh tattoo, this method also works well. Important to note that Black cattle do better with the greed ink, even hard to read tattoos can be seen with the use of a flash light placed behind the ear.
Also important when selling cattle to read the tattoo your self, and be sure you can read each digit clearly, if not when cattle are up having health work, you can fix what needs to be corrected.