A Tivo is probably not going to be adequate for your purposes. The problem would be distributing the channels to each TV and you wouldn't be able to watch a different live channel on each TV. Plus you'll have to pay their monthly premium for guide data or buy a lifetime subscription.
Your best bet currently would be 2 HD Homerun Primes or 2 Ceton InfiniTV4s with a single HTPC along with 4 Media Center extenders (generally an XBOX 360 but you can pick up some older Media Center extenders like the LinkSys or HP ones off of eBay). You could also use 2 HD Homerun Primes, 1 each with a separate HTPC for 2 of the TVs along with 3 extenders. I wouldn't recommend using 2 InfiniTV cards in separate HTPCs because, unlike the Prime, the Cetons don't have dynamic tuner assignment. You will also need a hardwired ethernet to each TV location along with a GigE switch to distribute the signals. If that isn't available it's also possible to use a MOCA setup over coax.
If you can wait a few months (or more, possibly to the end of the year), Ceton will be releasing their Ceten Q (a 6 tuner box that uses Windows 7 embedded) along with their MC extenders called the Ceton Echo. One advantage of that is you would only have to rent a single cable card and it would have enough tuners for all your TVs. The Q and Echos will also have a lot of other nice features that you can't currently get with cc tuners and extenders, like Internet browsers and access to some online services. The Q also has a BD player built-in.
For 5 TVs it is initially going to be an expensive outlay, probably ranging from $1200 - $1500+ depending on how you go with the extenders. If you don't have ethernet already in place their will be additional costs to set that up as well. However, with what FIOS charges for extra boxes, it would pay for itself in a year and a half or so. I've been using an InfiniTV4 and FIOS for a little over a year now (with just 2 TVs) and it has already payed for itself.
Be prepared to spend some time tweaking the system as well. It can be tricky at first learning the various hoops you may have to jump through ranging from getting the proper signal strength and SNR to configuring Win7 and 7MC correctly to avoid some common errors. Unfortunately it's not quite as easy as slapping in some cc tuners, hooking up your TVs over the network to extenders, and then kicking back. However, once you do have it set up it's a great system.
If you have any specific questions, feel free to PM me.