It would be very helpful to detail what "by the book" means.

What did you plant? 5 weeks is way too long for most plants. The seed packages often tell you how long before you will see a seed come up. About the longest I ever have to wait is 20 days---for carrots. A lot of things I plant are up by 10 days.

Did you plant too deep? Did you overapply fertilizer? Did you put dry peat in your garden?

Hmm. 10b. Does that mean Florida, or similar?

If you've had very dry weather for the past month your seeds may be still dormant and needing some moisture to get going.

If it has rained buckets - your seeds could have been either washed out or buried too deeply and rotted.

Did you buy seed suitable for your area? 10b seeds are for plants with different characteristics than those needed for plants grown in, say, 7a.

The tomato and the pepper: it sounds that you put in transplants. Unless they came in mini-pots and you planted directly, they may need to actually develop a good root system before they start showing top growth. Hope you planted the tomato deeply after taking off all the leaves EXCEPT the top four or five. That way the tomato can grow roots all along the stem and be sturdy in the ground.

Are they getting enough sun now? And water? And mild feeding?

Please let us know back.