Strength building from nothing, or close too is not going to be quick, especially close to having a child. Not the news you will want to hear but your son will gain weight faster than what you lift for a while, but you will catch up if you perservere.
Stomach flattening. Engaging core is the best thing you can do, absolutely spot on. The difficulty is that this need to be as constant as you can make it especially when seated or standing. As with any of the things I give you here if it hurts slowly relax out and stop, this isn't no pain, no gain because pain means gaining injuries.
The below is based on you having had an uncomplicated birth, not Ceasarian etc. If this is not the case don't do what I have advised unless you doctor thinks it is safe. You are at the start of one thing that will last a lifetime this is an intorduction to another.
This is not full on strength training, if you were to do that now you would be well placed booking a hospital bed in advance. This is known as muscular strength endurance training MSE, and will be light enough for you to do safely for reps and teach you the movements ready for more intense work in months to come.
This should last you 8 weeks or so at most and be at a level to leave you sore in the morning but not immobile or seriously hurting.
You mentioned having 5 pound weights, for now we will work with those. These are compound movements getting you used to some important movements and using your body as a unit rather than individual part. They will also challenge your core and help restrengthen this. The weight shouldn't feel too heavy, if it does do the movements without it just to familiarize yourself.
This is intended as a circuit, perform one exercise followed by the next in circuit, take rest if you need it but miss it if you can safely. Number of circuits is up to you, reps would ideally be around 15, anywhere between 10 and 20 is perfect. If 10 is too much drop the weight, 20 too easy, keep it going for a week or 2 then let us know.
Have at least 1 day rest between sessions, more if needed. There is nothing wrong with doing this once or twice a week, but everyday would be silly at first.
Deadlift with weights.
There is a wonderful video of me doing some really dreadful deadlifts recently on my journal and getting told what is wrong with them later in the thread. The below is how they are supposed to be done, I assume your weights are dumbells so this has you starting at the top of the movement.
Starting position
Feet hip width apart, feet flat on the ground, arms straight down, facing forward at a static point.
Movement
Keep your eyes fixed on the static point throughout, this will keep your back in alignment. Lead back with your hips, allowing the knees to bend naturally not forced, the hands stay in front of the legs as if you were holding a bar, and feet stay flat on the floor.
Finish point
This will be largely up to you. Deadlift is important as it teaches you how you should always lift from the floor so obvioulsy the lower you can go safely the better in some ways. However the further down you go the more chance of getting the movement wrong. I would say halfway to shins would be the furthest you should consider aiming for, but if getting to your knees is hard work and feeling unsafe don't even go that far. Movement will come with time.
Up movement is basically reverse of down with all of the body working in unison.
Push from wall.
This is basically push ups but instead of going from the floor you are pushing away from a wall.
Start position
Stand arms length from a wall with feet just over hip width apart, place hands on the wall shoulder width apart, bring feet half foot length back to put weight on hands.
Movement
Bend elbows to move your shoulders closer to the wall, hinge at the ankles keeping feet flat on the body as straight as possible.
Finish point
Again largely up to you, there is no minimum here, maximum is head having to move clear of the wall.
Intensity can be increased by bring feet further back if needed, but this shouldn't be too far as you will start feeling unstable.
Squats
Movement will seem very similar to the deadlift, but the differences of where you hold the weight and keeping lower back curved are important.
Starting position
Feet hip width apart, feet flat on the ground, hold weights at shoulders, facing forward at a static point.
Movement
Keep your eyes fixed on the static point throughout and your head and chest facing forward this will force your lower back to arch. Lead back with your hips, allowing the knees to bend naturally not forced, and feet stay flat on the floor.
Finish point
This will be largely up to you. If I started a thread about squat depth there would be arguments eternally, while you are building up initial strength I would say make maximum depth 90 degrees at knees and hips, you can increase this depth later to keep the purists happy. However if this feels unsafe don't even go that far. Movement will come with time.
Up movement is basically reverse of down with all of the body working in unison.
Plank from knees and elbows
This is a static exercise which will hit your core hard so keep the time safe. As soon as your body says enough relax out of the movement.
Getting into position
Slowly come down to hands and knees. Bring knees back to point where body is straight from knees to shoulders.
Pointers
Keep core tight, stomach pulled up. Relaxed breathing, don't hold your breath.
Coming out of the movement
Do not simply drop down, if you have to you waited too long in the plank position. Ideally reverse the process you did to come into it. If you can't push back through your hips to bend them and come up onto your hands.
This one is going to be very challenging to an area you have had weakened severely. There is a possibility you will not be able to do it at all, which you will notice as trying to get into position. If this is the case please let us know and we will give an easier alternative.
Google video search will show you some good technique on these exercises. If you are worried about your movement as I was when using new kit, put a video here for critique. It's better to be told where you are going wrong early than cause damage.
Gaining strength will take time especially this closely post natal if you aren't used to it. Patience will be key.