RCS (Red cherry shrimp) are one of the easier shrimp to keep and 1 female RCS can produce about 10-20 shrimpletts. If you want to limit your numbers-try to buy just males, however, baby shrimp are great food for the Betta-plus they give the Betta something to hunt. IMO five will be a good number to start with and depending on the cover-they may or may not do well with the female Betta. Every Betta can be different in their tolerance-some will hunt and kill every single one of them-while others could care less and you end up with a lot of shrimp.
In one of my 5gal NPT's that I use for spawning I have roughly 20-30 adult RCS that I have to thin out on a regular basis. The male Betta doesn't seem to bother them as much as the female-but I am sure they both eat the baby shrimp when they can find them.
If you have plenty of cover like java moss-you should still get some baby shrimp to survive. The baby shrimp are really tiny and usually the Betta will eat them first. Also, depending on the type of filter-with the HOB type the baby shrimp usually will end up in them-some survive the trip through the impeller and some don't-Its a good idea to check the filter box a couple of time a month. I have found large colonies of shrimp living happy in mine....lol.... Sponge filter are best for shrimp IMO especially in the smaller tanks. Its not uncommon for the shrimp to escape by crawling up cords and filter- especially if they feel threatened or bad water conditions.