Can I combine SRAM Rival 22 Levers and Shimano 105 Rim Brakes?

You will get brakes that work BUT won't be quite as the manufacturer intended because Shimano &SRAM use slightly different pull ratios. Campag and SRAM are supposedly the same, fyi.

Does that answer your question?

For BR-5700, BR-5800, and BR-R7000 they run off the various new school Shimano not-quite-short-pull cable travel numbers. SRAM road levers are all basically traditional short pull, which is less cable pull than Shimano Super SLR et al.

The mismatch in this direction results in less pad movement but with more leverage than intended. It can typically be made to work, but needs to run with commensurately smaller pad gap, which usually means the caliper QRs won't open up enough for an on-trend tire. Feel will be mushy and indecisive but power will be good as long as you can get the pads close enough that you don't bottom the lever. By the same token, you have less ability to use the Doubletap reach screw.

It does function, but it always feels like a way of making a mediocre system out of good components. The pre-5700 brakes are normal short pull.

While SRAM Rival 22 and Shimano 105 group sets are commonly considered to be at the same comparative level as far as performance, weight, cost and overall performance, that doesn't equate to their components potential to be successfully mixed. At least with an acceptable level of function. Whatever the system, it seems, mixing components from SRAM with Shimano ones, results in, at the very least, widely variable levels of workability and performance. Almost always, there results a diminished level of performance in mixed brand set-ups, the acceptability of which needs to be determined individually. The trend toward complete incompatibility is more prominent as successive generations--read, increasing number of rear drive speeds-- of components are brought to market. Thus, personally, unless an urgent situation forces the mix, it seems an exercise in folly to mismatch componentry when it can be avoided.

That said, the more recent generations of Shimano road brake levers have a longer pull than in the past and their rim brake calipers underwent associated design changes around the longer cable pull. This has essentially downgraded the braking performance of a SRAM--Shimano road brake system combination. It works, but not well, and in a system pretty important to the safety and well-being of the rider, I suggest it should be avoided. I'll note that earlier SRAM, Shimano, and even Campy brake systems all shared very similar cable pulls and mixing one brand's lever with another's caliper yielded nominal results. This is no longer the case beginning (IIRC) somewhere in the 10 speed generations. Definitely with any of the 11 speed group sets, mixing SRAM with Shimano brake components should be avoided, making the mix of a Rival 22 lever with a 105 caliper not advisable.

A popular cycling tips.com article discusses the permutations of Mixing Road Groupsets: What Works Together and What Doesn't. Brake systems are addressed near the end of the article.