I have a very similar situation. I have red Georgia clay. My bad field came back with a ph of 4.7 and my "good" field came back with 4.8 this is after applying 1ton of lime an acre. I would recommend finding a mineral for the animals that does not contain iron. Same qith their feed. I have sheep and I'm also currently looking for a mineral that contains no iron available in my area. Southern states has a 2:1 mineral that has no iron but no feed stores near me carry it. Which is strange as it would be one of the best for the cattle in my area.
1# get the iron out of their mineral and feed.
2# get the PH moved up.
I recommend having the lime spread for you. I purchased a herd 2500lbs spreader for lime and I would have to say I don't like it. Way cheaper/easier to have it spread. Though on just 5 acres you could do it with a push spreader and 50lbs bags. It would take a while maybe do a 1/4 acre a weekend. 10x50lbs bags. There is also coral calcium that can be sprayed on with water. I have not used it but a cattle farmer near me likes it.