The average selling price of houses in the District has risen only 5 percent in the past year -- the smallest increase for the city in nearly a decade, a new city survey shows.

In recent years, prices in many of the District's 56 neighborhoods had been jumping by 20 to 28 percent every 12 months. But "that sort of double-digit performance just couldn't continue with mortgage rates and the economy the way they've been," said George B. Altoft, the senior residential assessor who made the study.

Altoft's findings are based on data taken from all home sale transactions recorded in the District between January and July this year, excluding condominium and cooperative units. His statistics cover neighborhood-by-neighborhood price patterns, and are among the factors used by the city goverment to set future property tax assessments on every home.

Tax assessments could rise much more slowly here than in past years if the recent slow rate of appreciation continues through the rest of 1980.

The new study found that the number of sales in the District during the first six months of the year dropped by 20 percent from the first half of 1979 (1,966 transactions versus 2,462). The average price of a house sold between January and July was $94,750 -- up from $90,000 last year. During the first half of 1975, by comparison, the average sales price in the District was $42,000.

Prices of new homes sold in the city rose faster than the average for all dwellings, hitting $135,000 for the first six months, up from $107,000 during the same period in 1979. The volume of new home sales also was up -- from 121 to 147, a 21 percent jump.

Two strong patterns that emerge from Altoft's data are the relatively flat 1980 price levels in many of the District's upper-bracket Northwest neighborhoods, and the sizeable gains being posted in some of the more moderately priced Northeast and Southeast parts of the city.

Prices in Spring Valley, for example, rose only by 1.7 percent on average between 1979 and 1980, from an average of $232,000 for 20 sales in the first six months of last year to $236,000 for 12 sales in the first half of 1980.

Wesley Heights average prices rose by 2 percent ($196,000 to $200,000); Cleveland Parks's average dropped by more than 2 percent (from $209,000 in 1979 for 22 sales to $204,000 in 1980 for 17 sales). Burleith's average rose by 3 percent, as did Glover Park's and Berkley's.

Several Northwest neighborhoods -- particularly Foxhall (up by 33 percent) and Forest Hills (up by 36) -- racked up large average increases between 1979 and 1980, in part because of new construction.

But some of the biggest increases in the city during the year occurred in the Northeast and Southeast.

Marshall Heights in Far Southeast, for example, had the highest average price gain during the year -- 40 percent, up from $31,000 to $43,000. Riggs Park and Michigan Park, both in Northeast, jumped by 34 and 31 percent respectively during the same period.

Lilly Ponds in Northeast registered a 24 percent jump. Trinidad was up by 17 percent, Fort Dupont Park by 16 percent.

Altoft's study also found that:

Houses in 29 of the city's 56 neighborhoods now sell for an average of $100,000 or more, and 13 have average prices in excess of $200,000.

In some neighborhoods, prices have trippled in five years. Mount Pleasant's average price, for instance, went from $36,500 in the first half of 1975 to $115,000 in the first half of 1980 ($127,000 in the second quarter) -- a 216 percent rise, with virtually no new construction of units.

Three out of five of the neighborhoods that had the slowest appreciation rate from 1975 and 1980 are in Northwest: Wesley Heights (up 62 percent, from $123,000 to $200,000); Wakefield (up 64 percent, from $87,000 to $142,000), and Spring Valley (up 73 percent, from $136,000 to $236,000).

Condominiums, on a dollar-for-dollar basis, are out-performing houses in market value increases. Altoft released data two weeks ago showing that the average condominium in the city resold in the first half of 1980 had appreciated by 36 percent a year, or about 3 percent a month.