Your options as far as I know them, are:
1. You can get a 2.5" drive up to 3tb, replace it in the original configuration, and it will work right away.
2. You can get a 2.5" drive that will fit in the original configuration that is larger than 3tb, and if larger than 3tb (in 2.5" or 3.5" size) you will need to format it. Here is the free program and thread provided in this forum.
MFS Reformatter (mfsr) . You can really use any 2.5" hard drive, but there are only a couple of options for a SATA drive. Here is the only 5TB 2.5" drive that I know of (non SSD) Seagate Barracuda ($129 on amazon, not sure how that price compares). ST5000LM000
https://www.amazon.com/Seagate-BarraCuda-Internal-2-5-Inch-ST5000LM000/dp/B07MWDMD4J/ref=sr_1_3?crid=3E2PPIAE91BEH&keywords=seagate+barracuda+5tb+2.5&qid=1571065901&sprefix=seagate+barracuda+5tb,aps,160&sr=8-3
(The hard drives you find, and most of those listed, are not designed for 24/7 use. The constantly recording, and deleting type of use that a computer hard drive is not designed for.
3. You can buy a 2.5" Solid State Drive. You can find them 8TB, and higher, but you will spend $500-$1500 (or more if you really wanted to) for one. There is no advantage to having an SSD in a DVR like there would be in a computer. You are paying for the size only, and to have a drive that will fit in the factory location.
4. & 5. Both involve having an "external drive". For cost, options, and reliability, this would be a 3.5" drive. You can get 3.5" drives that are designed for AV or surveillance use. 3.5" drives are known to be a more reliable design. You can get a 3.5" drive in 8TB or more. and will cost about what a 4TB or 5TB 2.5" drive will cost. (I have read that 8TB is the cutoff, if you want more than that, then do some searching on this).
4. Would be to get an external drive. There are very few SUPPORTED on the market, and none are new. You connect it with your original drive installed. It will then pair to your drive, adding on that extra storage space. You will not lose your recordings when you connect, but you will if you ever disconnect. This is frowned upon, because if either drive ever goes bad you lose all your recordings. There is a program that is needed for the drive.
5. You can replace your hard drive with a 3.5" drive as your main and only drive. You have to remove the factory cables connected to your 2.5" drive, and run longer cables (through a modified TiVo case) to a drive that is placed externally. This allows you to use any 3.5" drive (size and style), it reduces the heat internally by removing the drive out of the case. The downside is you have a hard drive/or enclosure mounted somewhere near your TiVo, and have to make a hole in the case to allow the cable to pass through.
This is only meant to be a down and dirty explanation. Which ever method you choose, you should read more to feel 100% comfortable with your choice.