I've bathed 2 preschoolers at the same time and it wasn't too tiring. The kids were a bit older than yours. I'm wondering if including the 5 mos old baby is the extra that makes this not work. At 3 and 2 they are more independant. You don't have to watch them so closely so that they don't slip and fall. With the older ones in with the baby you have to keep the older ones less active. Having 3 kids in the tub at that age at the same time feels overwhelming to me. I'd bathe the baby another time; perhaps even another time of the day.
When my grandkids get rowdy in the tub we take one out. The next bath time, only one goes in at a time. Natural consequences sort of thing. If that time goes well we can try it again with 2.
Another thing that I do is I sit on the closed toilet and watch while they play for 15 or so minutes. Then I did the hair or any place that was still in need of soap.
My daughter gives her kids (8 and 5)a bath when she notices an odor or they're covered with dirt. I think they get a bath 3-4 times/week. She rarely has them bathe right before bedtime because they play off each other and get more energy. Now that they can pretty much bathe themselves one or the other sometimes takes a bath before dinner. They also take a shower with her sometimes in the morning. She started doing that when her daughter was around 3. I think she takes in one kid at a time so they both don't usually
have a bathe or a shower on the same day.
My daughter showers everyday. Kids don't have that odiferous perspiration problem that requires a more often bath or shower. Perhaps your husband could shower with one boy and you the other. At 2 both of my grandkids often sat at the foot of the tub with toys while Mom showered and then she held her/him to wash them.
If your kids have a bath often, say every 3 days or so, and if they're not outside playing in the mud there really isn't much to do in a bath. Playing in the water along with a couple of swipes with soap seems to clean them. If you use a soap or shampoo for babies their eyes don't sting even after it gets in the water.
Over the years how often one bathed has change. Way back people got a bath once a year. When I was growing up I had a bath once a week and so did everyone else I knew. When I was a preschooler we didn't have running water, which was somewhat common still, and so I probably didn't get a bath once a week even.
We had "spit baths."
My daughter does "spit" baths when there isn't time for the full bath and they're grubby, smelly. In the summer when the kids get really dirty feet I sometimes just have them one at a time sit on the edge of the tub while I wash their feet and legs.
I haven't found anything to use in the tub that quiets a child down. One at a time is usually easier.
My granddaughter, who's 8, takes a bath or shower to calm herself. She takes her Little Pet Shop animals with her and has wonderful creative conversations and action with them. She started that around 3 or 4. Before that age both kids had water toys to include a few plastic cups and bowls. Bath time was often play time. I sat and watched.