Q.is it typical for crepe myrtles to produce new growth from bottom up?
We have 2 crepe myrtles in full sun. They are 4-5 years old. Have never pruned them, but they are growing in very bushy at the bottom while the tall skinny branches from last year look dead. Should I cut off last here’s branches? Trim the new growth?

It sounds like your crepe myrtles were damaged somewhat by the winter -- that's why the tall branches are all bare, and the sucker growth from the stump and roots is abundant. But with some pruning, you can set your trees back on the road to their natural beauty. The first step is to remove all the dead branches, and cut the dead parts off the ones that still have life in them. Look for green tissue inside the twigs, or just under the outer cambium layer of larger branches and trunks. If the main trunk of the tree is still alive, proceed with pruning as in this article: https://www.gardeningknowhow.com/ornamental/trees/crepe-myrtle/pruning-crepe-myrtle-trees.htm
If there's nothing left alive but the suckers, you can still try to revive the trees, although it will take several years for them to regrow. Remove all but a few of the suckers. Leave the largest one, if you want to create a single-trunk tree, or the three or five largest ones if you want to create a multi-stem tree. Continue with good cultural practices, and prune your young tree as in this article: http://extension.oregonstate.edu/linn/sites/default/files/pruning_pub_handout2012.pdf