Study of variants in 2021 taught us a lot about what areas of the virus to look for with respect to change. Especially when small changes could make a big difference in slipping past an antibody response or becoming more transmissible in vivo. 

Two viruses dominated in 2021 and they were Delta and to a lesser extent Lambda. They have small changes that made the virus more transmissible and to a certain degree could reduce the potency of an antibody response by roughly 2 fold.
 
The arrival of Omicron BA1 and BA2 changed that dynamic at two levels. Both are marked by their ability to significantly evade a previous antibody response (through past infection and/or vaccine generated). Compared to the modest 2 fold drop in potency observed by Delta, these new variants resulted in a greater than 16 fold drop (Summarised here: https://twitter.com/StuartTurville/status/1483634549905330176?s=20&t=OZ7Gt2Be-QByRVDr0k7ghA and here https://www.medrxiv.org/content/10.1101/2021.12.14.21267772v1.full-text).
 
The other issue with Omicron BA1 and BA2 was that they changed the way the virus entered cells. In doing so, it meant the virus infects the upper respiratory tract far better (bronchial tissue), and the lower lung not as well. In animal models, this was observed to result in lower disease severity (https://www.nature.com/articles/d41586-022-00007-8).

So what is happening with BA4 and BA5 and another variant called BA2.12.1?
 
All have arisen from BA2 which has supplanted BA1 globally. BA2 won that race.

BA4 and BA5 have a small change in a part of the virus that in previous variants helped transmission and also enabled the variant to evade antibodies modestly. This was l452r and is present in Epsilon, Delta and Kappa.  

BA2.12.1 is similar but has the change that appeared in Lambda, l452q.

BA5 has another level of interest as it has the F486V change. We know changes around that same area can play a big role in antibody evasion, for example E484K was present in many previous variants that enabled them to be more "slippery" to antibody responses following infection and/or also vaccination.

Yet immune evasion doesn't always result in viral dominance.

Kappa was almost identical to Delta but it was more immune evasive with the E484K change. Delta didn't have that change but it was "fitter". It won by having a significant edge in the transmission stakes.
 
BA4, BA5 and  BA2.12.1, are examples of small changes in the right places. BA2 sublineages are  "whittling away" and are likely becoming fitter in the real world and displacing the original BA1 and BA2.

We will need to study this over time to see if their advantage is one of "fitness/transmissibility" and/or their ability to be more slippery to existing antibodies.

As with all variants, the key parameter to watch is disease severity and this data takes time to accumulate.

The key thing is that these are small changes in the virus, and not unlike what we have seen before. They may not resemble the large shift we saw with Delta to Omicron.

The key will be looking at pre-existing antibody responses to variants like BA4 and BA5 and there is data already coming out of South Africa (https://secureservercdn.net/166.62.108.196/1mx.c5c.myftpupload.com/wp-content/uploads/2022/04/MEDRXIV-2022-274477v1-Sigal.pdf). 
 
The other things to watch are the severity observations in animal models and if the virus has changed in how it is entering cells.

That is, does the virus infect the lung, like Delta, or is it infecting the upper respiratory tract, like Omicron BA1.

Then couple this information with how this manifests in the real world with respect to disease severity in those that have recovered from infection and/or have been vaccinated.
 
There is still a lot about this virus that is unknown and there are many paths it has the potential to take.