How can I deal with a non payer on a joint tenancy?

If the tenancy is joint and several, the 'tenant' is all five of the named individuals who jointly and severally have the obligation to pay the rent and perform the other tenancy obligations.
I have been in your shoes and have found that a private word to the non payer reminding them that you will seek payment from their guarantor and/or peers should they not step up does enough to frighten/shame them into payment. If it doesn't, then you can proceed to recover from the guarantor or other named individuals - whose own guarantors will be none too pleased should they get wind of the situation!

Hi, are the group all known to each other, ie friends? If they are I find that telling the non-paying tenant that all the other tenants will lose their deposits as they are in a joint tenancy, to cover his debt and that you will need to notify them of the situation, usually shames them into making payment arrangements pretty sharpish- hasn’t failed me yet!
Good luck

You say you have a Joint and Severally liable lease. This means one or ALL are responsible for this rent. If I were you I would send a statement to them all, as they are all liable, and could put pressure on the one who has not paid. You do not need to mention in your statement who is owing you rent, just the total paid and what is owing. They will quickly work that out!

I can only echo what the others have stated. All my ASTs have the 1st of the month for payment. After 5 days the tenant gets a polite but firm reminder. After 10 days, their guarantor and other housemates get a reminder with a full explanation. Only needs to happen once.

In future put the responsibility where it lies, have the leasd tenant collate the payments and make ONE transfer to you, it's their problem.

Joint and several means your claim would be against all 5 tenant deposits, and then against all guarantors - not just the non-payer's guarantor.
If the other 4 can't persuade the non-payer, I think it's unlikely you'll re-let to them. You'll incur legal costs, cost of new agreement, referencing etc. and there are emotions involved. You may want more rent to offset your costs. They might not want to pay more for the same as they had before. It's not a continuation because the non-payer forces one of the parties to suffer a loss.

In my experience joint tenants usually pool their rent money and make a single payment for the rent each month, although it sounds as though yours have been paying their rent individually.
Normally the AST Agreement states that the named individual tenants are jointly and severally liable for the payment of the rent - you have not said whether this is the case with your Agreement but others have assumed so because it's normal. If it is the case you must inform the other tenants of the position, because they are jointly liable for the shortfall in the rent as well.
The Agreement may say that it is for a Fixed Term but unless one party has given Notice then it will continue as a periodic tenancy when the fixed period expires at the end of this month because the notice period will be a minimum of one month from the next rent due date - and nobody has yet given notice. Check the Agreement to see what the notice period is - sometimes it's 2 months Notice from the Landlord and 1 month from the Tenant.
You're happy with the other four tenants so you need to discuss the situation with them, with the non-payer if possible, and try to reach an agreement for the non-payer to pay their outstanding rent and leave the property ASAP, so you can get a replacement tenant and sign a new Agreement with the 4 original tenants and the one new one. If necessary you may have to accept the non-payer leaving while still owing rent, but you need to involve her Guarantor in that case and make clear that you will pursue the outstanding debt through the civil court if necessary.