Hiya, I signed up to Cyclechat just to offer advice on this as I ride a Pashley E-type tandem and know that specific information on them is difficult to come across.
Many models and variations of each were made over the years, but I guess that with a 5 speed block and drum brake it is most probably ('thou not definitely!) a D-type.
All the suggestions above are to be considered and there are others. The rear wheels on these were generally fitted with heavy gauge spokes and, over time, these can distort the spoke hole in the hub due to the drum brake locking, resulting in movement of the spokes at the hub. The solution I prefer is to replace the rim, (alloy rims in 26 x 1 3/8 are easier to find now thanks to the internet...£20 - 25 should get a fair quality Rigida rim). Replace spokes with standard gauge laced in a four cross pattern, (about £10) this give a little extra strength which was previously given by the thick spokes. Use spoke washers (about £1 a set) at the hub end just in case some holes have distorted to allow the standard gauge head to pull through!
Adjust the drum brake so that it does not lock...the drum brake is to slow down on descents, if it is locking under load damage will be the result. Always apply the drum brake gradually so there is no sudden grab.
With regard to adjusting the bearings; some of the Sachs drum brake hubs were fitted with a special bearing cage that helps set the drum in the correct position. These are now impossible to find. If you have to replace the bearings, I have used 6mm (rather than the usual 1/4") and this positions the drum correctly without using the cage.
If you don't feel confident in doing this work yourself a good wheel builder should be easy to find...its not really that much different from any other wheel.
Hope this helps.