The most effective way for him to catch up to where he needs to be academically is to do additional work outside of school. Given that you say he is doing some year 5 work already, how willing / able are you to help him catch up to where he needs to be and how willing / able is he to put in the required work?
If this course is an option then you need to find out from the school if a) they would be willing to support you both in this endeavor and b) how far behind he is and exactly what he needs to achieve for them to support him rejoining his previous year group.
If I've understood correctly, he has issues that effect reading, writing and maths (dyscalculia)? Of these I think the maths is easiest to tackle independently at home, by doing some every day. For writing I suggest you get support from an Occupational Therapist that specialises in handwriting.
The reading is again something that you might need support with to find out the exact issues (for example how sound is his phonic knowledge and does he have issues with being able to track print with his eyes, leading to jumping lines and finding it hard to sound out long words systematically from left to right to name a few of the possible specific issues that might be inhibiting his progress).
It would be a significant endeavor requiring time and money (although there are ways to reduce costs e.g. by doing most assessments with him yourself with on-line support and using many of the excellent free or cheap resources available), however one to one work when willing undertaken (and maintained) is likely to result in him closing the gap at a surprising rate.
Whether this is fast enough given the time frame is another matter, which is why you need to talk to the school as this will allow you to know the extent of the task.
If this is not an option for you or your son doesn't feel willing to commit to quite intensive work over and above school / home work, then the alternative is to have an honest discussion with him about the likely outcome (that he must remain in the lower year group) and to support him emotionally with accepting that this decision, whilst not being what he wants socially, is best for him academically.
Then do as much as possible to support him developing the friendships with the pupils that he will remain with. If possible arrange at least some play dates / exciting activities to help him develop those relationships and have something to look forward to, especially over the summer holiday when he will be staying while his current friends will be moving onto year 7.
Apologies for the length of the post, I hope there's something helpful you can take from it!