I think he's beyond napping at age 5, so he is too awake and not tired enough to sleep. It's also completely normal for an inquisitive child to explore and try to do interesting things to see what happens - like mixing things he found in the cabinet, etc. It's possible that he's asserting himself as a "big boy" who doesn't need a nap when the baby naps. I know you are tired and want to nap with the baby, but maybe either you or your husband need to be awake with a 5 year old!
To start, give up the nap for him. He'll be more tired at night and perhaps he will not wake up. However, he's in the habit of getting up when he wakes up, so you need to re-train him that he stays in his room until it's light out or until an alarm goes off. There are all kinds of clocks and alarms that signal kids when it's an acceptable time to get up.
It's also time to reevaluate your home and where things are. You take things off the baker's rack, for example, and put them away. You put the things he's allowed to play with (plastic containers, etc.) in the low cabinets and you put the breakables or poisons or "off limits" things in upper cabinets with cabinet locks (available at any baby store or on-line child safety/parenting sites). You teach him how to climb safely. You encourage "science experiments" and exploration by having set times during the day when he can pick out the things he wants (within your limits) and play with a sink full of water with funnels and tubes and colanders. You teach him, however, that these occur frequently with parental supervision and during daylight hours, and absolutely never at 3 AM. You also teach him how (and require him) to put things back that he has played with. If it's more work to take things on his own, he'll eventually learn that it's better for him if he does it with you or Dad so the work is divided between 2 people.
If you have to put a lock on his door at night, fine. But explain that he needs his sleep and so do you. People who don't sleep can't drive cars or do anything else because it's dangerous to do things when you're not rested.
You'll have to do this in stages. Start with no nap and staying in the room until whatever acceptable hour of the morning you choose, plus putting on some cabinet locks. Make it reasonable. Before bed, he can choose some QUIET things to take into his room to play with in the morning if he wakes up before the acceptable hour. What he chooses are his playthings for the next morning. If you want him to have quiet time in his room during the day while the baby naps, fine - but don't require him to sleep. If he's sleeping at night and so are you, you won' be as tired during the day and needing a nap yourself. Then the baby's nap time can be special time with parent and 5 year old, something he looks forward to. If he knows he's going to get special time but only if he stays in his room at night, maybe he'll be more compliant. It may take some time, but if he knows that, no matter what, he will lose special time if he comes in your room to play at 3 AM, he'll figure it out.
After you solve the sleep problem, you can progress to teaching him the right skills to minimize injury. Some kids are athletic, climbers, explorers, etc. Mine was. The plus side is, these kids can be leaders, scientists, engineers, etc. We knew our son was going to be climbing the rock walls in between everyone's property (common in New England) and climbing trees. So we taught him to check for wobbly rocks and weak branches to keep him safer. We went on good bike rides, but only if he had a helmet (if he didn't, the bike went up in the garage rafters for 2 weeks). We did water play in the sink and outside, but only when it could be safe and not overflowing. We let him play with all kinds of things that weren't technically "toys" but not the important breakables. We worked out the limits and made it clear to him.
You can't protect him from everything but you have to get to the point where you are not so stressed out from lack of sleep that no one is having any fun. It's also okay to have a child earn privileges - let's see how you do with X, and then we can talk about progressing to Y and Z.