How do I beat a large Pokémon (that is 4-5 skulls of 31,000 CP) in a Pokémon GO Raid? If I solo it, I do not come close to beating it, even with maxed Pokémon.
You can't. If you pay attention to the suggested group size on the screen when joining a raid, it gives you a pretty strong hint:
The suggested group sizes are pretty conservative. If you're a high level player with good counters, you can do it with fewer people, but you still can't solo a tier 4 or 5, even at level 40. At level 40, you can solo any Tier 1 or 2, and some tier 3s. For more, see gamepress's guides:
Raid tiers 4 or 5 are too difficult to defeat by a single player. You should find other players to join you in the battle and help you defeat the raid boss.
Level 4 Raids are extremely difficult to Solo, and not all can be completed Solo. You will need to level up specific Pokémon with specific move sets for optimal DPS (damage per second), along with taking the Raid Boss' moveset and possible weather boost into consideration. Refer to GoHub's Raid Boss Guides for more info on optimal counters and strategies for each particular raid boss.
Even with two players, most Level 4 Raids are difficult. It is best to maximize your winning chances to encourage as many fellow trainers to join you as possible. Have you checked to see if your local city or community has a Facebook page or Discord group they use to coordinate raiding? This can help trainers immensely in winning raids and capturing better quality Pokémon to use in future raids.
I would like to build on the previous answers regarding the need for other players to assist you. In rural areas, this can be difficult to pull off, however the need for outside help is still going to be mandatory at Tiers 4 and 5.
To mitigate the need for large parties on those raids, you've a few options:
The release of the Friends function in the game can make a big difference on raids. As you increase your friendship level, you receive a damage boost whenever you take on a gym with your friend and that boost is not insignificant (as much as a 10% boost).
Perhaps you needed 4 or 5 people to take down a Tier 4 raid before Friends. Redoing the same raid with 2 of your Best Friends will become very viable due to the damage boost you get when raiding with friends.
One last note on Friends. It is not necessary that your friend be on the same color team as you. If you're on blue and your friends are on red and yellow, that's irrelevant for the purposes of granting the damage boost when doing raids.
In addition, weather impacts in your favor will also drive down the number of external help that you will need. If your attacking pokemon's moves align with the weather, that's another 20% damage boost.
Combining these effects can really drive down the number of outside help you will need for higher tier raids. In rural areas, it can be a lot more practical to get 2 or 3 of your friends together to help on a high tier raid than to hope you chance upon a group taking one on.