The LS3/5A was never easy to make. The design pushed 1970s drive unit, crossover and cabinet knowledge and technology to its limits. The design is not at all tolerant of variations in the drive units or component values. Several of the licencees failed to make any profit from the LS3/5A and the speaker was expensive to make and therefore expensive to buy. The 1978 Hi Fi Yearbook shows the list price of a pair of Rogers LS3/5As to be £152 including VAT. Compared to average earnings in 1978 they would cost a little over £1000.00 today.
If you want to build a pair of LS3/5A clones yourself then a good starting point are the links below. 
- Repair & What's Inside
- Peter Lotter's LS3/5A cabinet drawings
- Paul Whatton's thin-wall 15 ohm LS3/5As
- DIY Subwoofers inspired by the AB1
- External Crossovers for the LS3/5A
- The Chartwell Project Symphony Instructions
- Hi Fi Loudspeakers web site have the KEF Kit CS1 and CS1A construction leaflets as well as data sheets for the KEF B110 and KEF T27
- The Falcon Monitor Quality Compact.