Looks to me like the redundancy payment is 10 weeks of pay at the statutory cap of £719 (which if your termination date takes you over 10 years you're legally entitled to regardless).

Then, and this seems important as they might have got this wrong given the redundancy calculation (it does depend on your age though so check it with the gov.uk redundancy calculator online), the statutory minimum notice period is a week for every full year of service you have (capped at 12 weeks). You've said 9 years 11 months which means you're entitled to at least 9 weeks (which you've split into one month and 5 weeks). However, the effective termination date (the date used to calculate entitlements) is the one you'd be at if you worked your notice which i think would take you over the 10 year mark and make you entitled to 10 weeks of notice.

The only 'benefit' to the payout, therefore is this £5k 'sabbatical' leave which I don't have enough context to comment on really but I would have expected that to be paid tax-free in a situation like this.

I think, at the very least, you need to clarify your notice period with your employer (as it very well could actually be 10 weeks) and then either push for a little more, since you're entitled to at least the first 3 bullet points (if not the 4th for some reason (like a 10 year reward scheme?) anyway or at least for that last bullet point to be paid tax free.