CAT.M1 (a.k.a LTE-M) and NB IoT will continue into the future within the 5G specifications.
See also the link below to GSMA document addressing this:
https://www.gsma.com/iot/wp-content/uploads/2018/05/GSMA-5G-Mobile-IoT.pdf
Quote from page 7:
“3GPP has agreed that the LPWA use cases will continue to be addressed by evolving NB-IoT and LTE-M (CAT.M1) as part of the 5G specifications”
So for M2M the BG96 (NB IoT and CAT.M1 radios) will continue to be relevant for a long time yet, beyond the end of the decade and the eventual 4G sunset.
For higher data requirements (CAT1, CAT4 etc) will be served for many years by LTE and slowly phase into 5G after that. At present there are “Redcap” 5G modules (reduced capability, require 2 antennas) that are to replace the CAT1/4 devices in the 5G world. There are starting to be available now but need 5G SA (stand-alone) mode. SA mode will start to be deployed soon but will take some years to be widely available form of 5G.
In the natural order of progression of technology, 3GPP will evolve new standards for M2M use cases to migrate into the 5G evolution of Radio Access spectrum and core network. All this is in the future, at present BG96 (and later BG95) supports the M2M networks of LTE-M and NB IoT.
In other words, your customer does not need to worry that BG96, BG95 (BG77), BG95xA-GL will be obsoleted with impending 5G network roll-out.
CAT.M1 and NB1 (NB IOT) will evolve into CAT.M2 and NB2 with more functions for power saving and faster data rate. Future 3GPP standards, release 15 and onwards will integrate this radio technology into 5G core networks with lower latency.
3rd June 2020: Further underscored by Telstra directly in this article.
6th February 2020: Ericsson white Paper on Cellular IoT in 5G Era in this article
August 2022: 5G RedCap the new IoT Technology that shows the evolution of 5G to support simpler cheaper device requirements, eventually down to LPWAN (CAT.M1, NB IoT) integrated into 5G network. Article link. RedCap (Reduced Capability) is still in early stages in 3GPP Release 17, still has some way to go before standardising devices that are competitive to 4G LTE.