If you do this, how many ewes can you expect a tup to successfully cover? We usually have 15 ewes - would we insert 15 sponges one day then take five out on three consecutive days, all 15 on one day or what woudl we insert five songes on each of three days or what?
One ram can cover 10 ewes. A ram lamb can do only 5.
Your idea of taking out 5 sponges per day might work (or maybe you need to stretch to a two day gap) but you would be advised to hand mate - what I mean is supervise the mating so that he only mounts each ewe twice and is then removed from the ewes. That way he conserves his juice

. It's a bit time consuming, you'll need to pen your ewes and have a mating pen, release one ewe at a time into the mating pen, wait until he's served that ewe twice, then remove the ewe. Give him 5-10mins to recover, then repeat with the next ewe.
If it were me (and this is what I did last year), I would split the group up into two, and do 7 one week and 8 the next.. in fact I think I left it two weeks. Again, once he's mated all of the first group take him out. Once he's done all of the second group then put them all in together so that he can serve any if any repeat. This is also handy if you don't have many lambing pens

.
Alternatively, use two rams.
If you stagger the mating you will need to stagger the sponge insertion, unless its only a day or two's difference.
Cost of sponges is at least £50+VAT for a pack of 25 sponges. You can keep any spares for the following year. The applicator is about a tenner.