Q. I'm doing a 5x5. Do I need to do a valsalva for every rep and/or hold my breath for every rep?

No and no. There is no need to by worrying about a valsalva for the intensities encountered during a typical 5x5 and there is really no need to ever hold your breath. When you combine the volume and the relative intensity of a 5x5 you will get into much more trouble holding your breath than you would with just a maximal lift or very low reps.

When we encounter problems with blood pressure changes, which are one thing that can lead to exertional headaches, dizzyness and that kind of thing, it is usually volume related. Going up and down too fast and big changes in pressure due to the heavy lifting combines with a lack of time for normalization between reps. Holding your breath or attempting to do valsalva for every rep without a lot of control is not a good idea and really unnecessary.

If you do start to feel a headache coming on during higher volume but moderately heavy lifting, if it is not too late, pause at the beginning of a rep and take several shallow panting diaphragmatic breaths. The best way to describe this is the way women are sometimes instructed to pant while in labor. This helps to normalize blood pressure and may stop the headache from progressing. But if this doesn't work stop training immediately. If you allow a full-blown exertional headache to take place and try to train through it, which will be almost impossible, the pain can become agonizing and the residual pain may last up to an entire week. Not only that but you will not be able to train because even the slightest exertion will tend to bring on another episode during this residual time period.

Should you experience exertional headaches that you suspect are volume related, decrease the weight and volume and work back up slowly. You will adapt and should be able to get past the headaches eventually. Headaches can be caused from other problems, though, such as a pinched nerve in the neck and shoulder region.

2. Should I be breathing into my belly?

This is a trickier question. First of all "belly breathing" is really incorrect and a misunderstanding of the full picture. That is, the message that all the breath should be "taken into the belly" which results in an unnatural distension of the belly is incorrect.

People have misunderstood the problems with high chest breathing to mean that you should not be using you ribcage at all and instead should concentrate all breath to the belly. They think this is "diphragmatic" breathing.

Instead, correct breathing starts with the diaprhagm and then continues into the chest cavity..which I will explain in more depth in other articles. This kind of correct breathing does not result in the shoulder rising in excess. Indeed trying to artifically focus all breath into the belly could cause problems as well as there are a great many secondary muscles which contribute to breathing.

See Parodoxical and Diaphragmatic Breathing for further reading.