Read books 1-3. Then watch the show. Then see what people are saying about book 6 before deciding if you want to read books 4-5.
Books 4 and 5 were originally supposed to be one book, but it started getting ridiculously long. The way the books are written you get a chapter from the perspective of one of the main characters. Then the next chapter checks in on another character. So on.
Books 1-3 are well paced books with plenty of juicy bits.
When book 4 started getting way too long GRRM decided to split them up. He introduced a few new characters and basically just put one group of characters in book 4 then a separate group of characters in book 5 and the books are largely on parallel timelines. Obviously book 4 is shifted a little earlier and book 5 a little later, but there is significant overlap.
In books 4 and 5 GRRM gets REALLY bogged down as many of the main characters are on extended journeys all over the world. Trying to get someplace, trying to find someone, trying to escape, etc. The books (4 and 5) feel very much like everyone is just chasing their tails and never getting anywhere. There is a lot of important stuff that happens, a lot of good story, much of which the show has altered or cut out, but there's a lot of slogging through tediously chronicled journeys that makes them a bit of a chore to read.
I'm wondering if books 6 and 7 are being written much like books 4 and 5. If he is writing a lot of book 7 now. I actually really hope so for the sake of book 7 being released, but no one knows.